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Atlantic Energy Solar Reviews
When you make the decision to go solar, you're stepping into a whole new world. Because of that, you want to make sure you have a steady hand to guide you every step along the way. Atlantic Key Energy is Florida's top-rated solar company for a good reason, and our team takes pleasure in explaining everything you need to know. But don't trust us blindly – look through Atlantic Energy solar reviews and know you're making the right choice.
Atlantic Key Energy is a dependable solar energy company, with over 200 projects completed and a total of 8 awards. And not only that – it's important for us to know you're content with our work as well. For that reason, we are more than happy to listen to reviews and advice! We're delighted to see that Atlantic Energy solar reviews are so positive! Here's what our clients have to say about Atlantic Key solar systems and our services.
Many of our customers speak highly of our solar panels, and for a good reason. "You can help the environment, and save yourself some money," notes one of our clients. They also mention that it's silly not to go solar if you have the opportunity to, and if your roof qualifies for it. While savings are a common reason for using solar energy, customers say it's also good to know you're independent and have a reliable energy source at all times.
When it comes to using solar power, the Wagner family from Deland is quick to declare it the best. "We had so many issues with gas," the couple say, "but we never had issues with solar panels".
Finally, Mister Patrick McLean is quick to note how beneficial solar is for everyone. "Homeowners save money from day one, it creates jobs and boosts our economy, and saves the environment," he says. He's elated to be a part of that.
The Savings
The Wagners are happy to know the house will cost them virtually nothing now. Similarly, Cheryl Doll highlights solar power as a boon when selling a house. "Who doesn't want to go solar when it's already been done for you?" she says.
Cheryl also mentions how simple and cost-effective solar is. Since going solar, she noticed her savings have skyrocketed!
Our customer Dawn Artis notes that investing in solar panels was "reasonable, within her range". Not only do you save money, but the installation process is cheap as well!
Atlantic Key Energy Team
While our products are top-quality, our team hopes to make solar energy accessible for everyone. We make sure to approach our clients with care and help them with all they need. And our clients notice and appreciate that in their Atlantic Energy solar reviews!
Our Knowledge
First of all, you should know our experts are glad to help you understand how much money you're spending on energy – and how much you'd save by going solar! The Allen family and Brian Farney found this aspect of our service helpful in particular. It's clear that being well informed is useful when making a decision. That's why our team will gladly prepare a presentation to help you understand your expenses and savings.
Cynthia Fowler begins by saying that our team was not only nice and helpful, but ready to explain everything as well. She is glad that she is saving money and power, and thanks to our team, she can monitor her power use on all her devices as well.
Cynthia also says that she found our team's speed impressive. That is what pleased our other customers as well! They want to start saving as soon as possible, and Atlantic Key Energy is happy to help. Consequently, we aim to make this as smooth a process as possible.
Finally, when you make such an important decision, you want to do it yourself. We aim to give you space, but let you know everything necessary. The Wagner family mentions our workers are "nice, knowledgeable, not pushy." That's because we trust that our knowledge and approach will be the key to our partnership.
So, have Atlantic Energy solar reviews swayed you? If so, give us a call. This could be the beginning of a beautiful partnership!
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Category: Solar Energy September 9, 2020
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Home / Our performance / Property&Casualty segment / Operating result
The operating result for the property&casualty segment increased to € 1,831 million (€ 1,619 million at 31 December 2013). The significant increase observed (+13.1%) is mainly attributable to the technical result, with a Group Net Cor of 93.8%, improving by 1,9 p.p. compared to the previous year.
With reference to the fourth quarter of 2014, compared to the same period of the last year, the operating result increased (+5.3%), due to the development of the technical result in the fourth quarter.
The operating return on investments of the property&casualty segment increased to 4.70% (4.54% at 31 December 2013).
Technical result
(€ million)
FOURTH QUARTER 2014
1,082 794 205 78
Net earned premiums
19,622 19,788 4,927 4,902
Net insurance benefits and claims
-13,084 -13,552 -3,294 -3,424
Net acquisition and administration costs
-5,312 -5,372 -1,375 -1,376
Other net technical income
-144 -69 -53 -25
The technical result amounted € 1,082 million, registering a strong growth with respect to 2013 (+36.2%); the technical result includes the impact of catastrophic claims of approximately € 238 million. These events relate primarily to the floods that had repeatedly hit Italy in January, May, October and November and the storms of June in Central Europe. Similar events had an impact on 31 December 2013 for approximately € 460 million.
The worsening of the Other net technical income is primarily attributable to Italy for non recurring positive effects recorded in 2013 related to ceded reinsurance, as well as more reversal of previous years' premiums.
93.8% 95.6% -1.9
current year loss ratio excluding natural catastrophes
natural catastrophes impact
1.2% 2.3% -1.1
prior year loss ratio
-3.8% -3.4% -0.4
Acquisition cost ratio
Administration cost ratio
5.9% 5.9% 0.0
The combined ratio amounts at 93.8% decreasing of 1.9 compared to 31 December 2013, almost completely due to the improvement of the loss ratio (-1.8 pps); stable the expense ratio that is positioned at 27.1%.
In detail, the loss ratio registered a further improvement in respect with the results observed at the 3rd Quarter. This trend is also confirmed without considering the lower impact of catastrophic events, which weighted 1.2 pps with respect to the 2.3 pps in the previous year. The current year loss ratio excluding natural catastrophes, decreased by 0.3%; the contribution of the prior year loss ratio was also positive, which increases to -3.8 pps, in the context of the Group prudent reservation policy.
Net acquisition and administration costs amounted to € 5,312 million, compared to 31 December 2013 (€ 5,372 million). In detail, acquisition costs amounted to € 4,157, decreased of 1.2%, mirroring the trends registered in France, Central Eastern Countries, Switzerland and in the International Operations cluster. The incidence of acquisition costs on net earned premiums is slightly decreasing to 21.2% (-0.1 pps).
Administrative costs amounted to € 1,155 million, evidencing a decrease of -0.7%, mainly because of the observed effects of Italy, Germany and Switzerland. The ratio of expenses to net earned premiums remained stable at 5,9%.
The expense ratio remained stable at 27.1%.
A review of the combined ratio for the business areas of the Group will follow.
The ratio in Italy improved considerably (-3.2 pps), amounting to 89.2%. This trend mainly reflected the decrease in the loss ratio (−3.6% pps) which benefited from the positive trend of non - catastrophic events. Catastrophic claims increased, amounting to € 96 million (1.7 pps on the net cor; 0.5 pps at the end of 2013) due to the floods of January, October, November and the storms in July. The expense ratio increased with respect to the previous year, amounting to 22.1%, due to the increase in acquisition cost.
The combined ratio of France is equal to 104.9%, evidencing a decrease of 0.6 pps with respect to the previous year due to the contraction of the loss ratio, equal to 77.2% (-0.7pps). This ratio includes the impact of 2.4 pps of the catastrophic events, caused by the floods of January and the storms of June, while the impact in the prior year was of 2.8 pps.
The current year loss ratio, excluding natural catastrophes was stable. The positive trend of the retail line is absorbed by the considerable amount of claims in the auto-fleets line. Negative contribution from the prior year loss ratio considering the strengthening of the reserves related to the Buildings and General lines, likewise the observed trend of the market. Stable the expense ratio at 27.7% (+0.1 pps).
The combined ratio of Germany amounted to 92.6, strongly decreased with respect to 31 December 2013. Previous year suffered from significant catastrophic events, which weighted for 4.1 pps (1.1 pps at year end 2014). Non catastrophic claims were stable.
The expense ratio decreased by 0.2%, at 28.3%.
CENTRAL AND EASTEN EUROPEAN
The combined ratio of the central and easten European countries was 87.7%, decreasing slghtly with respect to 2013 (-1.0 pps).
This ratio includes the impact of the catastrophic events of 0.4 p.p., while last year catastrophic events influenced the ratio for 4.1 pps.
Expense ratio experience (31.9%) a slight drop of -0.2 pps compared with prior year.
The combined ratio of the regional structure EMEA was 95.5%, improved slightly compared to 31 December 2013 (-0.3 pps) due to the trends observed in the main markets of the area.
The combined ratio of Spain, equal to 93.3, improved (-1.0 pps) due to the contraction of the loss ratio (-0.8 pps) and to a lesser extent to the expense ratio (-0.1 pps).
The combined ratio of Austria also improved (-0.4 p.p.), reaching 94.2% due to the decrease in the loss ratio (66.9%), despite some reserve strengthening which weighted for 1.2 p.p.
The combined ratio of Switzerland, amounting at 92.7%, registered an improvement (-1.7 pps) due to the positive trend (-2.5 pps) of the expense ratio, which amounts to 22.6%. The claim rate increased (+0.9 pps).
The combined ratio of Latin America increased by 12.4%, amounting to 113.3%, because of the trend of the Brazilian cor, which suffered from worsening of the claims rate on the motor line, caused by a specific line of business in run-off.
Financial result
Investment result
1,007 1,012 218 255
Current income from investments
Other operating net financial expenses
-352 -398 -83 -94
The financial result amounted to € 1,007 million, stable with respect to 31 December 2013 (-0.5%). In particular the current income from investments amounted to € 1,358 million (€ 1,410 million at 31 December 2013); this decrease is mainly attributable to the difficult context of low reinvestment rates. The actions of the Group, aiming at sustaining the result have allowed the achievement of a current return of 3.3%.
In detail, the change in current income is primarily attributable to the decline in income from real estate investments - net of amortization - decreasing from € 283 million at 31 December 2013 to € 268 million.
Despite the low reinvestment rate context, income derived from investments in fixed income securities registered a stable trend in line with the previous year, amounting to € 863 million at 31 December 2013 to € 861 million in 2014.
The current income from equity instruments, instead, recorded an increase at € 121 million (€ 94 million at 31 December 2013). Other operating net financial expenses, which include interest expense related to operating debt and investment management expenses amounted to € -279 million (€ -325 million at 31 December 2013), due to lower interest expenses on operating debt.
Operating result: Other operating items
Other operating items of the property&casualty segment, which primarily include non-insurance operating expenses, depreciation and amortization of tangible assets and multi-annual costs, provisions for recurring risks and other taxes, increased to € -258 million (€ -187 million at December 31, 2013) mainly due to increasing provisions for risks.

redpajama_set_name: RedPajamaCommonCrawl


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Q: Difference between probability and likelihood I had to think through what it meant when I read that likelihood is not probability, but the following case occurred to me.
What is the likelihood that a coin is fair, given that we see four heads in a row?
We can't really say anything about probability here, but the word "trust" seems apt.
Do we feel we can trust the coin?
Found on internet.
Probability quantifies anticipation (of outcome), likelihood quantifies trust (in model).
I Can someone give clean explanation.

A: Probability is the quantity most people are familiar with which deals with predicting new data given a known model ("what is the probability of getting heads six times in a row flipping this 50:50 coin?")
while,
Likelihood deals with fitting models given some known data ("what is the likelihood that this coin is/isn't rigged given that I just flipped heads six times in a row?").
A likelihood quantity such as 0.12 is not meaningful to the layman unless it is explained exactly what 0.12 means: a measure of the sample's support for the assumed model i.e. low values either mean rare data or incorrect model!
"https://www.youtube.com/watch?v=pYxNSUDSFH4" can be helpful

redpajama_set_name: RedPajamaStackExchange


Tracking Engineering Skills Over Time | Kids Engineer!
I am trying to think of a good way to track engineering skills over time. I will be tracking this year's K class as they progress to sixth grade. Is there a task I can give them that will work over all these years? I thought making a chair (from the Tufts CEEO first grade lesson) but could it involve robots later? Ideally, it was be the same or similar so we could easily see the changes but what would work over such a long time and such a change in development?
This entry was posted in Child Development, Robotics. Bookmark the permalink.
While I'm not (yet) doing a study over years of time, this school year has morphed into a study of 3rd, 4th, & 5th grade "above average" students in my resource room pullout enrichment program. Somehow we got to talking about Rube Goldberg Contraptions and now each class is trying to learn about simple machines, how to get from here to there, AND get along with each other. Rule of my class is All for One (YOU) & One (YOU) for All. The goal is to participate in the Goob Roldberg Fair (Show off for parents) in spring. Rules are you must create whatever on a 36 X 48 piece of pegboard base (so it'll be movable). Clean out closets, drawers, garage & bring in stuff! Must have at least 10 steps and use each of 7 simple machines at least once. No animals or hazardous parts allowed. Goal is to fill my picnic basket (with nerf balls). I provide the base, the basket and balls. Right now we are exploring with K'nex, Dominos, Legos (motorized, not NXT, yet), Zome, & Uberstix. Each class has a crate with poles with which to make marble run prototypes. Oh, and the artistic ones are being encouraged to draw what they are finding out, Goldberg-style, for the brochure for the fair. There's bunches of Goldberg contraptions on YouTube and Bill Nye has some great video about simple machines. We film every time they have a success and hopefully will be able to create something dynamic. Sorry, too much info just to suggest you might consider a Rube Goldberg Contraption as a yearly project.
Found your blog by following a link from the LEGO Engineering Google group.
Interesting problem. Do you give an engineering design challenge in September and the same design challenge the following May? Your results may be skewed because in May, they're doing a challenge have already experienced.
If you give them a different challenge in May, how can you determine that the two challenges are roughly equivalent?
And what should you be looking for? The number of ideas generated in brainstorming would be easily quantifiable. If the challenge was to design a catapult, for instance, you could compare outcomes by measuring the resulting throws. But I would also want to evaluate how well the students engaged in the engineering process, and that would seem more difficult to quantify.
Thanks for writing, Peter. The idea was to give a yearly task to show growth (or not) over time as they experience our main robotics/engineering curriculum every year. Specifically, how do their engineering design skills change as they get older and get more experience. Thanks for the ideas about quantifying some of this.


When it comes to decorating a space, I am all but clueless on most fronts. I've had the same furniture pieces and framed photographs for the last who knows how many years, and now that I'm trying to be an adult, I can use all the help I can get with choosing accent pieces and not-IKEA furniture.
Enter Megan Hopp, interior designer extraordinaire (check out her *ah-mazing* home tour). Today we're stepping inside her beyond gorgeous New York office and asking her 10 of our most perplexing decor and design questions. So imagine you're taking a seat as her new client and take in all the fabulous tips and tricks on how to decorate our spaces like a pro.
Help! I've got kids/a pet/a dirty roommate, but I *love* white furniture. Can I have it all?
Having a low maintenance room that is light and bright is doable! Having a white couch that stands up to stains is not. No matter what, white furniture is something to be careful with. Sure, certain fabrics are a little easier to maintain than others, slipcovers can be washed, etc., but when it comes down to it, a white couch requires a certain set of behavior and care.
However, you know what doesn't require a ton of work? A light grey or light beige couch! I highly recommend selecting grey or neutral upholstered furniture and then using white in other elements of the room, examples being: paint color, window treatments, and all other non-upholstered furniture. Your light grey couch will suddenly feel lighter and brighter than you had ever imagined.
Where should I look for furniture investment pieces? Which pieces do you recommend I splurge on?
Your sofa! Non-negotiable: your couch, sectional, or sofa is the most important piece to invest in. My rule of thumb is that upholstered, a piece's quality is directly related to cost, whereas in dealing with wood, metal, stone, and any other hard material piece, you can get quite clever with lower cost options.
What's the key to a great gallery wall?
Have at least one throughline. Maybe this means all the frames are walnut, or all the art is black and white photography — have at least one running theme that each piece holds true to.
Hang an odd number of frames, whether that be three or twenty-three. I say that decorating is much like comedy in terms of the "rule of three" — an odd number is always better looking (probably funnier too).
Speaking of three, think of creating your gallery in terms of three different size groupings; small, medium, and large. You only need a few large pieces (often just one, depending on the size of your gallery), then fill out the combination with mostly medium size pieces, and finish up with a moderate amount of smaller frames.
My living room is tiny — how do I make it intimate but not crowded?
My answer to small spaces often comes back to "You don't need as much as you think." People get it in their head that a living room has a certain list of pieces that NEED to be there (two armchairs, a media console, a coffee table), I think this theory comes from living room layouts on sitcom sets! Give the room just enough, and not anything more than it can realistically accommodate.
You will enjoy your space more, and it will serve you better if you let the room dictate how the layout will go. Not every room can fit everything, so I urge clients to be open to re-thinking what is absolutely necessary to have in their space.
My living room is massive — how do I embrace the spacious and also bring it all together?
Like the question above, the reverse is true also. People will say to me, "Oh but I don't need any more seating," and I say "But your room most certainly does!" Again I tell clients to drop the formula — design is SO far from one size fits all.
Top pieces to think about in a large space are appropriately sized area rugs (nothing kills me more to see a little 5×8 rug drowning in a big open room). Large lighting is very important (this goes for overhead, wall, table, and floor) — tiny lights in a large room do not support the space.
How do I light different spaces if I don't have recessed lighting? Where do you recommend I look for affordable lighting fixtures?
I never did meet a table lamp I didn't love — okay, that might not be true, however, I LOVE LAMPS, and I don't think people use enough of them. Truly, I do not think you need overhead or wall lighting to make a space chic and well balanced in terms of light. I advise clients to put lamps in places other than on a side table. Tops of bookcases are great, pianos, wall shelves, mantles, you name it. All this is to say, survey every surface you have in the room and make a plan accordingly.
In terms of affordable lighting, Target remains a favorite spot to look for lamps at a really great value. I also HIGHLY advise hitting your local thrift store — lamps are not difficult to rewire, so no need to worry about whether or not it even works.
Finally, I would like to talk about battery-operated lighting options. There are products on the market that are battery-operated pendants and sconces you can attach to your walls and ceiling wherever you like!
This pendant is a personal favorite of mine, and I use it constantly. However, I'm not done yet. I rip off (I mean carefully remove) the original pendant shade and replace it with some sort of attractive drum or orb shade, and the result looks just like this.
What are some easy tricks to make a room look pulled-together?
Paint the walls: Something different, or a better version of what you have now, an example being turn your "kind of white" walls into WHITE walls.
New floor coverings: A new area rug can COMPLETELY change a room, and can bring out a new look in your already existing furniture.
Different art & wall decor: Whether it be re-arranging, adding new pieces, or completely starting from scratch, what's on your walls can definitely change the space.
Rearrange your furniture: Of course this only applies to rooms that have enough optionality to allow for this; however, if you do, it's a refresh that will give you a new perspective.
Switch up the palette: Do you have blue pillows and accessories? How about swapping them out for green and grey pieces instead? Simply changing the palette of the "small stuff" can make the big picture shine a different hue.
What colors are best for what rooms?
For small rooms (especially those with low ceilings), I always recommend darker, more vibrant colors, as well as wild and crazy wallpaper prints. Small rooms are to be thought of as a juice glass quantity of color and pattern — very concentrated and bold.
Medium size rooms, as you might have guessed, are the most flexible in terms of light to dark, pattern, or no pattern. Of course it depends on the specific details of the space, but generally speaking, there are really no pitfalls here.
In large rooms, I lean toward lighter colors and simpler prints (see where I'm going here?). A big open room is a great opportunity to go white. I also like to stick to neutral shades in large spaces and use color through other elements of the space like window treatments or accent decor. I prefer large scale or geometric prints when it comes to wallpaper in a big room — a small pattern over and over for miles on end is far too dizzying.
What suggestions do you have for someone looking to slowly update their spaces? Where's a good place to start?
I don't have the most fun answer for this question. I would love to say something like "Go buy a few new vases today, in a month throw in some pillows, and presto!" I fundamentally do not feel that way about decorating and design. I live by the big-to-small trajectory of a space, meaning start with large pieces, move into accent furniture, and finish up with lighting and decor. Some people have a real knack for this kind of thing and can move through the process a bit more willy-nilly, but for most folks, big to small is the key to a well-thought-out room.
The second part to this is that when you are not buying everything all at once, you don't need to have a full scope plan prior to the purchase of your couch. You can start with just one piece — just make sure it's central to the space (and that you love it). From there, build brick by brick, making sure that each new piece fits in the puzzle you have previously put together. As you might imagine, flexibility and optionality will narrow as you move through the process, but by the end, your vision should be clear enough that selecting those finishing touches will be the obvious icing on the cake.
What's the simplest way to elevate a room?
Updated lighting, in any and every place you can put it, is the fastest way to make a dynamic change in a space — and this goes for every single type of room in a home. In bathrooms, I find that people just don't "decorate" at all, they pick the tiles and the floor, and the vanity, and then stop. Wall decor, shelving, accessories and textiles are such important tools to take your bathroom from forgettable to noteworthy.
Finally, don't forget about the space in your place that lives above 32" off the floor! The most common thing I see at the start of a project in bedrooms, offices, living, and dining rooms is a bunch of furniture that is all the exact same height (and not very high at that). Use your walls, please, I beg of you! It's more of a hassle (I know) to mount a bookcase or hang that large mirror, but your room will thank you, and you will then thank your room.
I rent my apartment/house. How can I update my space without adding paint or putting big-time holes in the walls?
I suggest LARGE leanable or freestanding pieces in a rental space where you don't want to get into the business of getting friendly with your walls. If a gallery wall feels like a move you don't want to make, find a long console table and several pieces of tall and sizeable art to lean and layer across the width of the table to create the same look and feel.
Same with shelving — maybe wall-mounted storage and display is too invasive, so look for open bookcases or etageres, then try pairing two or three of them together side by side for a "built-in" and more substantial look. Ask yourself "what is the other way" I can make this happen?
In your opinion, what design trends are not worth investing in/do you wish would just disappear?
I hate microfiber. It's not making anyone's life better.
Shop Denim Mini Skirts, Printed Jumpsuits, Black Sneakers, Ripped Skinny Jeans and more. Get this widget.


The total program fee is $750 per student including coach bus transportation. The program fee includes lodging, most meals, and program expenses for the entire week. Students should bring between $30 and $40 for meals to and from CONA and any incidentals students may want to purchase at CONA.
This program fee is at a discounted rate for 2019, to encourage participation from Kansas students.
After students are selected, a $100 non-refundable deposit will be due by March 29. The remaining balance of $650 is due by May 1.


Neuronox is a product similar to Botox, a Botulinum toxin type A based product, which is derived and purified from Clostridium botulinum. The main function of botulinum based products is to be injected into muscles and block their ability to contract. The application of such products is both medical and cosmetic, as they have been known to successfully treat conditions like migraine. However, they are most popular as a powerful means for cosmetic corrections and anti-age product.
Neuronox is injected into the patients muscles in order to locally reduce muscle activity. The practical effect of injecting the botulinum product is inhibiting the release of acetylcholine.
As a means for treating medical conditions, Neuronox has been successfully applied to patients suffering from hemifascial spasm, blepharospam and cervical dystonia. But it is also very potent in shaping facial lines, hiding wrinkles and other signs of aging.


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Ravens give defensive back Tavon Young contract extension
OWINGS MILLS, Md. (AP) — Baltimore Ravens defensive back Tavon Young has signed a three-year contract extension, part of the team's effort to retain budding talent.
The 24-year-old Young had one year left on his rookie contract, but first-year general manager Eric DeCosta wanted to get a jump on keeping the slot cornerback.
DeCosta says he "talked a few weeks ago about keeping our best young players, and Tavon is the definition of that."
After spending the entire 2017 season on injured reserve with a torn ACL, Young played in 15 games last season despite being bothered by a groin injury. He had 34 tackles, an interception and two fumble returns for touchdowns.
The 5-foot-9, 185-pound Young was selected in the fourth round of the 2016 draft after playing at Temple.
In his two seasons as an active player, Young has 86 tackles, two sacks, three interceptions and three fumble recoveries.
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Peter Okoye unveils former Kush singer, Emem Ema, as his new manager – Royal Times of Nigeria.
Peter Okoye now known as Mr. P, has unveiled Emem Ema as his new manager.
Emem was a member of gospel group KUSH that comprised of Emem, TY Bello, Lara George and Dapo Torimiro.
Emem boasts of nearly a decade of artiste management experience. Shortly after bagging a law degree from the University of Lagos, she started her talent management firm, One Management and she's worked with superstars like Joseph Benjamin and many others in the past.


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Emma Thompson made a dame in Queen's Birthday Honours
The actress has already received a string of accolades during her glittering career.
One of Britain's most acclaimed actresses, Emma Thompson has been a stalwart of the big and small screen since the late 1980s but has maintained an un-starry air throughout her dazzling career.
It is for her services to drama that the star, 59, has earned a damehood in the Queens's Birthday Honours list, continuing a long list of achievements that includes Oscars, Baftas, Golden Globes and Emmys.
She has also enjoyed success at the box office and with critics, with literary adaptations such as Sense And Sensibility; for which she won an Oscar for writing the adaptation; Howards End; which scored her a best actress Oscar, and The Remains Of The Day as well as crowd-pleasers such as Love Actually, the Nanny McPhee films, which she also wrote, and the Harry Potter blockbusters.
Emma Thompson in Sense And Sensibility (Sony)
Born in 1959 to an acting parents – her mother is Phyllida Law and her father Eric Thompson narrated the English version of The Magic Roundabout – Thompson became a self-proclaimed feminist while reading English at Newnham College, Cambridge.
It was there she also discovered a love of performing and joined Footlights alongside Stephen Fry and Hugh Laurie.
Her professional breakthrough came in 1987 when she starred in Fortunes Of War and Tutti Frutti, the former opposite Kenneth Branagh, who would go on to become her first husband.
Emma Thompson with Kenneth Branagh (Adam Butler/PA)
Her relationship with Branagh, to whom she was married between 1989 and 1995, was as professionally productive as it was romantic and she starred in a string of his Shakespearean adaptations on stage and screen, including Henry V, A Midsummer Night's Dream, King Lear and Much Ado About Nothing.
At the 1994 Oscars, Thompson became the eighth performer in history to be nominated for two statues in the same year, when she scored a best actress nod for The Remains Of The Day and a best supporting actress nomination for In The Name Of The Father, in which she starred opposite Daniel Day-Lewis.
One of her biggest commercial successes came in 2003 in Love Actually, in which she suspects her husband (played by Alan Rickman) of infidelity.
She has said this is the role she gets commended for more than any other.
Emma Thompson, Hugh Grant and Keira Knightley at the Love Actually premiere (Ian West/PA)
Famously fun-loving, she earned even more fans when she walked on to the stage of the Golden Globes in 2014 carrying her high heels and a martini.
Also an outspoken human rights activist, she is a supporter of the Labour party and a campaigner for Greenpeace.
She still lives on the road where she grew up in London with her husband Greg Wise, whom she met while filming Sense And Sensibility.
Emma Thompson with husband Greg Wise, second left, daughter Gaia and adopted son Tindyebwa Agaba at the Baftas in 2014 (Ian West/PA)
The couple have a daughter Gaia, 18, and a son, Tindyebwa Agaba, a Rwandan orphan they informally adopted in 2003 when he was 14.
08 June, 2018 21:30 Entertainment


Chick-peas cooked with fresh onions, tomatoes and potatoes.
Fresh cauliflower & potatoes cooked with choice of Indian spices.
Okra sauteed with browned onions, tomatoes.
Baked eggplant cooked with onion, tomato and ginger.
Fresh green peas cooked with lightly fried Indian cheese.


Hormel Food Corp.'s (HRL - Get Report) shares held steady Friday morning after news that its Jennie-O brand is voluntarily recalling thousands of pounds of turkey products out of concern they may be linked to the recent outbreak of Salmonella bacteria.
By noon, shares were trading up around 1%, closing at $45.89. But the news is still a setback for the brand, just before the Thanksgiving holiday, with some 91,388 pounds of ground, raw turkey products getting recalled.
USDA investigators, along with the Centers for Disease Control and Prevention and the Arizona Department of Health Services, had tested unopened Jennie-O brand turkey from the home of a patient who fell ill and it matched outbreak strain, prompting the recall, according to the USDA.
All of the turkey products were produced on Sept. 11 and have use-by dates of Oct. 1 or Oct. 2, according to the, U.S. Department of Agriculture's Food Safety and Inspection Service.
Though poultry was old, some people may still be storing it in their freezers, and if so, should return it or throw it away, says the USDA.
"On behalf of the thousands of Jennie-O team members, we were concerned to learn that someone became ill after exposure to Salmonella in a raw turkey product," said Steve Lykken, president of the Jennie-O Turkey Store, in a statement, adding that the turkey industry has been working to reduce Salmonella contamination and that the "issue of Salmonella isn't specific to Jennie-O."
Some 164 people in 35 states have been sickened by the current outbreak of the so-called Reading strain of the bacteria, according to the CDC. One person has died and dozens more have been hospitalized.
Eating food that's been contaminated with Salmonella can cause diarrhea, stomach cramps and fever within 12 to 72 hours. While the severity can vary, the sickness can last up to 7 days.
Hormel will release its fourth-quarter earnings report Tuesday.


text:
"I don't mind a reasonable amount of trouble"
Opposition pols: Put those calculators down, and speak the truth
Jul 13, 2019, 7:08 PM
In veritas, win (Dan Perry photo)
There are two ways to win elections: scheming, and leading. Both can win you votes; only one wins you dignity. Benjamin Netanyahu's rivals have been losing with indignity. That has driven malaise and despair, and explains the interest in Ehud Barak, whose jackhammer message that the emperor has no clothes has the pleasing tenor of unabashed truth.
In the coming September election, the opposition enjoys impressive advantages.
Every living former military chief opposes Netanyahu, four of them on the front lines with guns blazing, each in his own way. Three indictments await him, including on bribery. And he was caught red-handed trying to engineer immunity for himself, immediately after polls closed in April, despite fervent campaign promises not to do so.
Moreover, Avigdor Liberman appears to have amputated himself and his Russian immigrant backers from Netanyahu's right-religious bloc. For the opposition, that turned defeat into a 60-60 tie in terms of Knesset seats, and made the former bouncer a legitimate candidate for history's strangest deus ex machina.
The country is as an angry wounded beast, rising on hind legs and thrashing in all directions to cast off the flawed but brilliant monkey clinging desperately to its back.
It may still all end in tears, unless the challengers mend their ways.
Scheming these days takes the form of obedience to consultants and pollsters with their data and deep dives pulling campaigns toward what has worked before. Vision falls well outside their scope of work, but politicians listen anyway.
They will tell Netanyahu's rivals to not risk upsetting his backers by quoting the attorney-general's scathing accusations, even though this leaves a huge bag of cash on the table. They will also counsel against running on specifics and push for a generic timidity that breeds evasiveness in interviews, drives no momentum, and builds no sort leadership that a human might observe.
This is different from defensible centrism, such as if the U.S. Democrats chose Joe Biden over a "progressive" in 2020. The center can be a better path, more electable and wiser both. But muzzling even the center in hopes of offending no one is how we got a somnambulant campaign in Round One. And that was a waste, because the opposition had finally wheeled out a very big gun: the consensus of the generals.
Over the years of Netanyahu it became clear that the heads of the security establishment mostly opposed his agenda, especially the making permanent of Israel's hold on the West Bank but also on his reckless gamble to fight the nuclear deal with Iran (they certainly understood that Netanyahu's insistence that the deal allowed Iran to race to a bomb upon expiration was untrue).
Israeli society may not lionize "the generals" as in the past, which is good, but people will certainly pay attention to them. Until 2019 this advantage of the center-left amounted to another bag of cash left on the table. But daintiness was finally case aside in the creation of Blue and White, and here are the results:
_In the 2015 election, 2,376,498 people voted for the right-religious, meaning 56.5%. Of these, 451,756 voted for Haredi parties, meaning that with them the non-Haredi right got 1,924,742 votes. Meanwhile, 1,824,500 voted for the left-Arab bloc, meaning 43.5%, but a quarter of those went to the United Arab List; excluding it the "Zionist left" got 1,373,616 votes.
_In the 2019 election, 2,391,968 voted for right-religious bloc (including parties that did not get in), meaning 56.8%, slightly higher than before. Of that, 507,324 voted for Haredi parties, where all the growth was; removing them, the right got 1,884,644, or 40,098 fewer than in 2015. On the other side 1,814,467 voted for the left-Arab bloc, of which 388,447 voted for the Arab parties (62,437 less than before); so without the Arab parties the "Zionist left" won 1,426,020, an increase of 52,404.
The Blue and White leadership seems pleased with its 35 seats out of 120, tied with Likud, even though their bloc lost (before the Liberman defection yielded a tie). That came from siphoning most Labor votes from 2015 on top of Yesh Atid's base. Blue and White was actually meant to increase the bloc from 53 in 2015 to 61, but what was achieved was an increase of just 1.3%, or about 50,000 votes, or about two seats.
And even that modest gain was wiped out by the reduced Arab turnout, from over 60% in 2015 to under 50% in 2019. The reasons include funding woes, anger at the United List for splitting, and a misguided reaction to the Nationality Law (they viewed it as formalizing their second-class status but by boycotting the election they rewarded Netanyahu for it). It probably also relates to Blue and White's refusing to engage them (although, to be fair, the feeling was mutual).
Blue and White did not invent this; Labor reeked of in its short-lived rebranding as the "Zionist Camp." The "center-left" acts this way because it sees that two-thirds of Israel's Jews have voted for the right-religious bloc in every election since 2001, and loses hope (the exception was 2006 election when Ariel Sharon's Kadima reshuffled the deck by speaking the truth). That the right contains the religious sector with its dramatic population growth breeds despair. So they don masks, hope for the best, and get their butts kicked, again and again.
The question on everybody's lips this week is which groups will unite and who will lead which subgroup; this is important, but it is another form of scheming. I am here to say ideas are important no less.
My advice (full disclosure: I have offered it directly) has been to speak the truth, because it is right and more likely be work. The main potential messages enjoy support among Israeli Jews. That will make inroads among many who vote by default for the right but are not radical, and energize a base that has been abandoned.
"Centrist" messages might include:
_ Haredim: Nowhere in the world are religious Jews a dependent class as they insist on being here. Workarounds might be found for the army, partly because the army cannot meet their gender segregation demands, but some form of national service is essential. The Haredim must enter the workforce in normal numbers and the state cannot subsidize schools that do not teach math, science and English. A majority of Israeli Jews agree with this.
_ Russian immigrants: You are disproportionately secular, law-abiding and educated, and many appear to be fiercely patriotic new Israelis. The right-religious bloc is turning Israel into a non-Western, non-Jewish, non-secular place. Backing them you align with people who think Israel doesn't need tanks as long as yeshiva students pray. Liberman, who has helped this cabal for decades, is not the right address. You belong in the center-left.
_ Israeli Arabs: We want to embrace you. Please be as the Hungarian minority in Romania or the Turkish minority in Bulgaria — different, but accepting of the majority group's right to have one place under the sun. Your second-class status will be totally over, your funding will be equal and perhaps preferential, and we will want you at the cabinet table and in the highest of offices. National service would be nice.
_ Zionists: We will look for ways to separate truly from the Palestinians of the West Bank. While apartheid is not an accurate word for what goes on there, neither is the situation just or sustainable. Even if a peace deal is not possible now, Israel will ceaselessly seek solutions to avoid absorbing 3 million more Palestinians. And it will stop pouring billions upon billions into the settlements; that is a fool's errand. A majority of Israeli Jews agree with this.
_ Likudnik democrats: This business of overriding the Supreme Court with a simple majority of Knesset members is the end of checks and balances. You know it; don't support it.
_ Consumers: Israel is not the economic success that Netanyahu claims. The per capita GDP is similar to France's only because of the artificially strong shekel that devastates your purchasing power and puts Israel among the world's most expensive countries, higher than all in Europe outside Switzerland and the wealthy-heavy Nordics, whose people get services you do not. It can be different: the vast majority of the land is the state's, and the state can break crony monopolies, reform taxation, stem waste and accelerate construction.
If the opposition leaders did this, they would lose the racists and Haredim just like their lame advisers warn. That's a phantom loss: the votes aren't actually there. In exchange there would be gains all over the map. In exchange, they might inspire.
And if they went down anyway, they would be going down swinging. Ask any slugger: it is the better way.
Dan Perry, a media and tech innovator, was the Cairo-based Middle East Editor of the AP, and chairman of the Foreign Press Association in Israel. Previously he led AP in Europe, Africa and the Caribbean. Follow him at: twitter.com/perry_dan www.linkedin.com/in/danperry1 www.instagram.com/danperry63 https://www.facebook.com/DanPerryWriter/
2019 Israeli elections
Arab Israelis
Israel: Jewish and Democratic
Ultra-Orthodox Jews
On charismatic rabbis and cults
Yosef Blau
Pinchas, Tsnius, and the Perils of Intolerance
Golda Daphna


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text:
\section{Introduction}
\label{intro}

Low-dimensional correlated spin-electron systems, which are rigorously treatable by means of the standard transfer-matrix method~\cite{Bax82} and/or the generalized decoration-iteration mapping transformation~\cite{Syo72}, represent an excellent play-ground for theoretical investigation of many unusual cooperative phenomena. Despite of their simplicity, these models may provide novel insight into macroscopic degeneracy of the ground state~\cite{Per08, Per09, Nal14, Cis14, Gal15a, Gal15b, Str16, Gal17}, rational~\cite{Per08, Nal14, Gal15a, Gal15b, Gal17} and irrational (doping-dependent)~\cite{Str16} plateaus in low-temperature magnetization curves, entanglement properties~\cite{Nal14}, double- and triple-peak structure in temperature dependencies of the specific heat~\cite{Per08, Nal14, Gal15a, Cis14}, as well as enhanced magnetocaloric effect~\cite{Per09, Gal15a, Gal15b, Str16, Gal17}. Moreover, hybrid spin-electron systems with the geometry of decorated planar lattices quite well demonstrate the presence of the spontaneous long-range order in the ground state~\cite{Gal11} and also uncommon reentrant phase transitions at non-zero temperatures~\cite{Dor14}.

Motivated by aforementioned facts, in the present paper we investigate an exactly solvable double-tetrahedral chain, in which nodal lattice sites occupied by the localized Ising spins regularly alternate with triangular clusters with the dynamics described by Hubbard model (see Fig.~\ref{fig:1}). As recently shown~\cite{Gal15a, Gal15b, Gal17}, this hybrid model provides an excellent prototype, which allows a rigorous study of the macroscopic degeneracy at absolute zero temperature, the associated residual entropy, as well as other thermodynamic quantities. Another important stimulus for investigating the aforementioned model relates to the copper-based polymeric compound Cu$_3$Mo$_2$O$_9$~\cite{Has08, Mat12}, which represents the experimental realizations of the double-tetrahedral chain structure.

\section{Model and its exact solution}
\label{sec:2}

To be specific, we consider a spin-electron double-tetrahedral chain defined through the Hamiltonian:
\begin{eqnarray}
\label{eq:H_tot}
\hspace{-3mm}
\hat{{\cal H}}\!\!\!\!&=&\!\!\!\! \sum_{k=1}^N \hat{{\cal H}}_k,
\\
\hspace{-3mm}
\label{eq:Hk}
\hat{{\cal H}}_k\!\!\!\!&=&\!\!\!\!
-\,t\sum_{j = 1}^3\sum_{\gamma\in\{\uparrow,\downarrow\}}\left(\hat{c}_{kj,\gamma}^{\dagger}\hat{c}_{k(j+1)_{\rm mod\,3},\gamma} + \hat{c}_{k(j+1)_{\rm mod\,3},\gamma}^{\dagger}\hat{c}_{kj,\gamma}\right)
\nonumber \\
\hspace{-3mm}
\!\!\!\!&&\!\!\!\!
-\, J\hat{S}_k^z(\sigma_k^z + \sigma_{k+1}^z) - \mu\hat{n}_k - H_{e}\hat{S}_k^z - \frac{H_{I}}{2}(\sigma_k^z + \sigma_{k+1}^z).
\end{eqnarray}
In above, $N$ represents the total number of nodal lattice sites occupied by the localized Ising spins $\sigma=1/2$ ($N\to\infty$), $\hat{c}_{kj,\gamma}^{\dagger}$ and $\hat{c}_{kj,\gamma}$ mean fermionic creation and annihilation operators for mobile electrons delocalized over $k$th triangular cluster with the spin $\gamma\in \{\uparrow,\downarrow\}$, respectively, $\hat{S}_k^z = \sum_{j = 1}^{3}(\hat{n}_{kj,\uparrow}-\hat{n}_{kj,\downarrow})/2$ labels the $z$th component of the total spin operator, $\hat{n}_{k} = \sum_{j = 1}^{3}(\hat{n}_{kj,\uparrow}+\hat{n}_{kj,\downarrow})$ denotes the total number operator corresponding to electrons in $k$th triangular cluster ($\hat{n}_{kj,\gamma} = \hat{c}_{kj,\gamma}^{\dag}\hat{c}_{kj,\gamma}$) and $\sigma_{k}^{z}= \pm 1/2$ marks the Ising spin occupied the $k$th nodal lattice site. The term $t>0$ represents hopping parameter, which takes into account the kinetic energy of mobile electrons, $J$ stands for the exchange interaction between mobile electrons and their nearest Ising neighbors and $\mu$ is the chemical potential allowing one to tune the total number of electrons in the system. The last two terms in Eq.~(\ref{eq:Hk}) represent Zeeman energies of mobile electrons and Ising spins in a presence of the 'effective' magnetic fields $H_{e} = g_e\mu_{\rm B}B$ and $H_{I} = g_I\mu_{\rm B}B$ ($g_e$ and $g_I$ are Land\'e g-factors of electrons and Ising spins, respectively, $\mu_{\rm B}$ is Bohr magneton). Finally, the modulo 3 operation is introduced into Eq.~(\ref{eq:Hk}) to ensure the periodic boundary condition $\hat{c}_{k4,\gamma}^{\dagger}=\hat{c}_{k1,\gamma}^{\dagger}$ ($\hat{c}_{k4,\gamma}=\hat{c}_{k1,\gamma}$) for the three-site electron subsystem.
\begin{figure}[t!]
\vspace{0mm}
\centering
  \includegraphics[width=0.4\textwidth]{figure1.eps}
\caption{(Color online) A part of the spin-electron double-tetrahedral chain. Full circles denote nodal sites occupied by the localized Ising spins $\sigma = 1/2$ and empty circles forming triangular plaquettes are available to mobile electrons.}
\label{fig:1}
\end{figure}

The cluster Hamiltonian~(\ref{eq:Hk}) can be written as $64\times64$ matrix if a number of mobile electrons at each triangular plaquette varies from zero up to six. Thanks to a validity of the commutation relations $[\hat{{\cal H}}_k, \hat{n}_{k}] = 0$ and $[\hat{{\cal H}}_k, \hat{S}_k^z] = 0$, the matrix representation of the Hamiltonian~(\ref{eq:Hk}) has the block-diagonal form. Individual matrix blocks correspond to the orthogonal Hilbert subspaces with different but fixed numbers $n_k$ of mobile electrons and distinct values of the total spins $S_k^z$. Diagonalization of these blocks gives a full spectrum of eigenvalues for the cluster Hamiltonian~(\ref{eq:Hk}), which can be further employed both for a comprehensive analysis of the ground-state configuration and an analytical calculation of the grand-canonical potential of the model:
\begin{eqnarray}
\label{eq:Omega}
\Omega\!\!\!\!&=&\!\!\!\!
-k_{\rm B}T\!\lim_{N\to\infty}\frac{1}{N}\ln\Bigg[\!\sum_{\{\sigma_k\!\}}\mathrm{Tr}\,{\rm exp}\left(-\beta\hat{{\cal H}}\right)\Bigg]
\nonumber\\
\!\!\!\!&=&\!\!\!\!
-k_{\rm B}T\!\lim_{N\to\infty}\frac{1}{N}\ln\Bigg[\!\sum_{\{\sigma_k\!\}}\prod_{k=1}^N\mathrm{Tr}_k\,{\rm exp}\left(-\beta\hat{{\cal H}}_k\right)\Bigg]
\nonumber\\
\!\!\!\!&=&\!\!\!\!
- k_{\rm B}T\ln\bigg\{v(1) +\! v(-1) + \!\!\sqrt{[v(1) \!-\! v(-1)]^2 \!+\! 4v(0)^2}\bigg\},
\end{eqnarray}
where
\begin{eqnarray}
\label{eq:w}
\hspace{-2mm}
v(x) \!\!\!\!&=&\!\!\!\! \frac{1 + z^6}{2}\,{\rm exp}\left(\frac{\beta H_Ix}{2}\right)
\nonumber\\
\hspace{-2mm}
\!\!\!&&\!\!\!\!+
\Bigg\{(z\!+\!z^5)\left[{\rm exp}\left(2\beta t\right) \!+\! 2{\rm exp}\left(-\beta t\right)\right]\cosh\left[\frac{\beta (Jx\!+\! H_e)}{2}\right]
\nonumber\\
\hspace{-2mm}
\!\!\!&&\!\!\!\!+
(z^2\!+\!z^4)\left[{\rm exp}\left(-2\beta t\right) \!+\! 2{\rm exp}\left(\beta t\right)\right]\cosh\left[\beta (Jx\!+\! H_e)\right]
\nonumber\\
\hspace{-2mm}
\!\!\!&&\!\!\!\!+
\frac{z^2\!+\!z^4}{2}\Big[4{\rm exp}\left(-2\beta t\right) \!+\! 4{\rm exp}\left(\beta t\right) \!+\! {\rm exp}\left(4\beta t\right)\Big]
\nonumber\\
\hspace{-2mm}
\!\!\!&&\!\!\!\!+
z^3\cosh\left[\frac{3\beta (Jx\!+\! H_e)}{2}\right] \!+\! 5z^3\cosh\left[\frac{\beta (Jx\!+\! H_e)}{2}\right]
\nonumber\\
\hspace{-2mm}
\!\!\!&&\!\!\!\!+
4z^3\cosh\left(3\beta t\right)\cosh\left[\frac{\beta (Jx\!+\! H_e)}{2}\right]\Bigg\}\,{\rm exp}\left(\frac{\beta H_Ix}{2}\right).
\end{eqnarray}
For more computational details see Ref.~\cite{Cis14}, which deals with similar hybrid spin-electron model having the linear chain structure. The summation $\sum_{\{\sigma_k \}}$ emerging in Eq.~(\ref{eq:Omega}) includes all possible states of the localized Ising spins, the symbol $\mathrm{Tr}$ labels for a trace over the degrees of freedom of all mobile electrons in the model and $\mathrm{Tr}_k$ stands for the partial trace running over degrees of freedom of electrons from the $k$th triangular plaquette. The symbol~$\beta=1/(k_{\rm B}T)$ represents the inverse temperature ($k_{\rm B}$ is Boltzmann constant) and the parameter $z = \exp(\beta\mu)$ appearing  in Eq.~(\ref{eq:w}) denotes the electron fugacity.

\section{Ground state}
\label{sec:3}

In this section we will discuss a diversity of the ground state in dependence on interaction parameters of the model and the applied magnetic field. Due to fundamental differences between magnetic behavior of the system with distinct nature (sign) of the spin-electron coupling $J$, the analysis will be divided into two parts; the case of the ferromagnetic ($J>0$) and antiferromagnetic ($J<0$) exchange interaction. To reduce the number of free parameters, equal 'effective' magnetic fields acting on the Ising spins and electrons $H_I=H_e=H$ will be assumed in both the cases.

\subsection{The ferromagnetic exchange interaction $J>0$}
\label{subsec:31}

Typical ground-state phase diagrams of the model with the ferromagnetic spin-electron interaction $J>0$ in the $\mu-H$ plane are illustrated in Fig.~\ref{fig:2}. Obviously, the displayed phase diagrams are symmetric with respect to the line $\mu = 0$ and contain eight different ground-state phases, which can be characterized by the following eigenvectors and ground-state energies:
\begin{eqnarray}
\hspace{-6mm}
\label{eq:S_0,2,4,6}
|{\rm S}_{a}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm S}_{a}\rangle_k  = \prod_{k=1}^N\left\{  \!\!\begin{tabular}{l}
                                                            $|(\downarrow)\!\uparrow\rangle_{\sigma_k}$
                                                            $\!\otimes$
                                                            $|n_{k}=a,S_{k}^{z}=0\rangle$,\, $H = 0$
                                                            \\[1mm]
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=a,S_{k}^{z}=0\rangle$\hspace{3mm}  ,\, $H > 0$
                                                     \end{tabular}
                                        \right.\!\!\!\!,
                                        \nonumber\\
                                        \hspace{-6mm}
E_{a} \!\!\!\!&=&\!\!\!\! -\frac{N}{2}\left[ H + 2a\mu + a(6-a)t\right],\,\,\, a=\{0,2,4,6\};
\\[1mm]
\hspace{-6mm}
\label{eq:S_1,5+}
|{\rm S}_{b}^{+}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm S}_{b}^{+}\rangle_k =
\prod_{k=1}^N\left\{      \!\!\begin{tabular}{l}
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=b,S_{k}^{z}=-\frac{1}{2}\rangle$ ,\,
                                                            $H = 0$
                                                            \\[1mm]
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=b,S_{k}^{z}=\frac{1}{2}\rangle$\hspace{3mm}  \hspace{-1mm}, $H \geq 0$
                                                     \end{tabular}
                                        \right.\!\!\!\!,
                                        \nonumber\\
                                        \hspace{-6mm}
E_{b}^{+} \!\!\!\!&=&\!\!\!\! -\frac{N}{2}\left( J + 2H +2b\mu + 4t \right),\,\,\, b=\{1,5\};
\\[1mm]
\hspace{-6mm}
\label{eq:S_3+}
|{\rm S}_{3}^{+}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm S}_{3}^{+}\rangle_k =
\prod_{k=1}^N\left\{ \!\!\begin{tabular}{l}
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=-\frac{3}{2}\rangle$ ,\,
                                                            $H = 0$
                                                            \\[1mm]
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=\frac{3}{2}\rangle$\hspace{7mm}  \hspace{-5mm}, $H \geq 0$
                                                     \end{tabular}
                                               \right.\!\!\!\!,
                                                \nonumber\\
                                                \hspace{-6mm}
E_{3}^{+} \!\!\!\!&=&\!\!\!\! -\frac{N}{2}\left(3J + 4H + 6\mu\right);
\\[1mm]
\hspace{-6mm}
\label{eq:S_3chiral+}
|{\rm \widetilde{S}}_{3}^{+}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm \widetilde{S}}_{3}^{+}\rangle_k =
\prod_{k=1}^N\left\{ \!\!\begin{tabular}{l}
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=-\frac{1}{2}\rangle_{L, R}$,\,
                                                            $H = 0$
                                                            \\[1mm]
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=\frac{1}{2}\rangle_{ L, R}$\hspace{2mm}, $H \geq 0$
                                                     \end{tabular}
                                               \right.\!\!\!\!,
                                                \nonumber\\
                                                \hspace{-6mm}
\widetilde{E}_{3}^{+} \!\!\!\!&=&\!\!\!\! -\frac{N}{2}\left(J + 2H + 6\mu + 6t\right).
\end{eqnarray}
In above, the product~$\prod_{k=1}^{N}$ runs over all elementary unit cells, the state vector $|\!\uparrow\rangle_{\sigma_k}$ ($|\!\downarrow\rangle_{\sigma_k}$) determines up (down) state of the Ising spin at the $k$th nodal lattice site, while $|n_{k}, S^{z}_{k}\rangle$, $|n_{k}, S^{z}_{k}\rangle_{L,R}$ refer to the non-chiral and chiral eigenstates of $n_{k}$ mobile electrons in the $k$th triangular plaquette with the total spin $S^{z}_{k}$, respectively. Analytical expressions of the state vectors $|n_{k}, S^{z}_{k}\rangle$, $|n_{k}, S^{z}_{k}\rangle_{L,R}$ are too cumbersome for some electron concentrations, therefore we omit them in this work. Finally, the subscripts $a$, $b$, $3$ specify a total number of electrons per triangular plaquette in individual phases, and the superscript 'plus' in the phases~(\ref{eq:S_1,5+})--(\ref{eq:S_3chiral+}) points out to the same signs of the total spin of electron plaquette and the state of the Ising spin that form $k$th elementary unit, i.e. it is a result of the product ${\rm sgn}(S_k^z)\cdot{\rm sgn}(\sigma_k^z)$.
\begin{figure*}[t!]
\centering
\vspace{0.25cm}
\includegraphics[width = 1.0\textwidth]{figure2.eps}
\vspace{-0.5cm}
\caption{\small (Color online) Ground-state phase diagrams of the model with the ferromagnetic spin-electron interaction $J>0$ constructed in the $\mu-H$ plane for three representative values of the hopping term. The blue solid, red dashed and green dot-dashed lines denote first-order phase transitions with the macroscopic degeneracies ${\cal W} = 2^N$, $3^N$ and $4^N$, respectively.}
\label{fig:2}
\end{figure*}

As can be understood from Eqs.~(\ref{eq:S_0,2,4,6})--(\ref{eq:S_3chiral+}), the arrangement of the Ising spins depends on a presence of the magnetic field and the total spin of triangular plaquettes. To be specific, the first group of phases S$_{a}$, within which triangular plaquettes have zero total spin, because they are either empty, fully-filled or partly occupied by two or four electrons in a quantum superposition of several non-magnetic and intrinsic antiferromagnetic states, exhibits a kinetically-driven frustration of the Ising spins at the zero magnetic field. As a result, the residual entropy per elementary unit ${\cal S} = k_{\rm B}\!\ln 2$ can be observed for $H=0$, which indicates the zero-field macroscopic degeneracy ${\cal W} = 2^N$. An arbitrary non-zero field cancels this degeneracy, because it forces all the Ising spins to align into its direction.
On the other hand, if triangular plaquettes are occupied by odd number of electrons, as it is in the phases S$_{b}^{+}$ and S$_{3}^{+}$, all the Ising spins in the model may occupy either the down or up states with the same probability if $H=0$. Mobile electrons in triangular plaquettes also choose between two possible quantum states with the total spins $S_{k}^{z}= -1/2$ and $1/2$ (in S$_{b}^{+}$) or between two classical ferromagnetic states corresponding to the total spins $S_{k}^{z}= -3/2$ and $3/2$  (in S$_{3}^{+}$) in order to preserve the spontaneous ferromagnetic order with the nearest Ising neighbors. Any non-zero magnetic field lifts this two-fold degeneracy of the phases S$_{b}^{+}$, S$_{3}^{+}$. Last but not least, there can also be found a peculiar field-independent macroscopic degeneracy if the phase ${\rm \widetilde{S}}_{3}^{+}$ constitutes the ground state. It is valuable to point out that ${\rm \widetilde{S}^{+}}_{3}$ is the only one ground state from the group of phases~(\ref{eq:S_0,2,4,6})--(\ref{eq:S_3chiral+}), in which the entropy per unit cell remains non-zero in the whole parameter space. The observed value ${\cal S} = k_{\rm B}\!\ln 2$ is a result of two possible chiral degrees of freedom ($L$eft- and $R$ight-hand side) of mobile electrons in each triangular plaquette. We note that the phase ${\rm \widetilde{S}}_{3}^{+}$ and the phases S$_{2}$, S$_{4}$ can be identified in the ground state just for the hopping terms~$t/J>1/3$ (see Fig.~\ref{fig:2}).

In general, the high macroscopic degeneracy can also be found at points of discontinuous (first-order) phase transitions, where different ground states are in thermodynamic equilibrium. Positions of these points can be identified by comparing the ground-state energies of individual phases. Namely, macroscopic degeneracies of three different sizes ${\cal W} = 2^N$, $3^N$ and $4^N$ may be observed along individual phase boundaries. The first degeneracy can be found along the phase transitions S$_2$--S$_4$ and S$_p^{+}$--S$_{p\pm1}$ ($p=\{1, 5\}$), while the second one
corresponds to the boundaries that separate the chiral phase ${\rm \widetilde{S}^{+}}_{3}$ from the neighboring non-chiral ones S$_2$, S$_4$ and S$_3^{+}$. The last (highest) degeneracy can be found at two special phase transitions S$_q^{+}$--S$_{q+2}^{+}$ ($q=\{1,3\}$), which are marked as green dot-dashed lines in Fig.~\ref{fig:2}. At each point of these boundaries, spin-electron configurations of elementary unit cells corresponding to the neighboring phases S$_q^{+}$, S$_{q+2}^{+}$ are in thermodynamic equilibrium with another (novel) configuration ${\rm \widetilde{S}}_{(q+1)k}^{+}$ given by the following eigenvector and ground-state energy
\begin{eqnarray}
\label{eq:S_2,4chiral+}
|{\rm \widetilde{S}}_{q+1}^{+}\rangle_{k} \!\!\!\!&=&\!\!\!\! \left\{ \begin{tabular}{l}
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=q+1,S_{k}^{z}=-1\rangle_{L, R}$,\,\,\,
                                                            $H = 0$
                                                            \\[1mm]  $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=q+1,S_{k}^{z}=1\rangle_{ L, R}$\hspace{2mm},\hspace{2mm}\,$H \geq 0$
                                                     \end{tabular}
                                               \right.\!\!\!\!,
                                                \nonumber\\
\widetilde{E}_{(q+1)k}^{+} \!\!\!\!&=&\!\!\!\! -J -\frac{3H}{2} - (q+1)\mu  - t.
\end{eqnarray}
Similarly as the phase ${\rm \widetilde{S}}_{3}^{+}$, the configurations~(\ref{eq:S_2,4chiral+}) are macroscopically degenerate due to the chiral degrees of freedom of mobile electrons. Their existence along the phase boundaries  S$_q^{+}$--S$_{q+2}^{+}$ causes the double increase in the macroscopic degeneracy compared to the boundaries, where two non-chiral ground states are in thermodynamic equilibrium.

\subsection{The antiferromagnetic exchange interaction $J<0$}
\label{subsec:32}

In agreement with general expectations, more complex ground-state behavior can be observed for the model with the antiferromagnetic spin-electron interaction $J<0$. In fact, a~mutual competition between the parameters $t>0$, $J<0$, $\mu$ and $H\geq0$ generates three novel non-chiral and one novel chiral magnetic phases at the zero temperature apart from those found for the ferromagnetic version of model. These phases are unambiguously characterized by the following eigenvectors and ground-state energies:
\begin{eqnarray}
\hspace{-6mm}
\label{eq:S_1,5-}
|{\rm S}_{b}^{-}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm S}_{b}^{-}\rangle_k =
\prod_{k=1}^N\left\{      \!\!\begin{tabular}{l}
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=b,S_{k}^{z}=-\frac{1}{2}\rangle$ \\[1mm]
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=b,S_{k}^{z}=\frac{1}{2}\rangle$\hspace{3mm}
                                \end{tabular}
                                        \right.\hspace{-4mm},\,H \geq 0,
                                        \nonumber\\
                                        \hspace{-6mm}
E_{b}^{-} \!\!\!\!&=&\!\!\!\! \frac{N}{2}\left( J -2b\mu - 4t \right),\,\,\, b=\{1,5\};
\\[1mm]
\hspace{-6mm}
\label{eq:S_3-}
|{\rm S}_{3}^{-}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm S}_{3}^{-}\rangle_k =
\prod_{k=1}^N\left\{ \!\!\begin{tabular}{l}
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=-\frac{3}{2}\rangle$ ,\,
                                                            $H = 0$
                                                            \\[1mm]
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=\frac{3}{2}\rangle$\hspace{7mm}  \hspace{-5mm}, $H \geq 0$
                                                     \end{tabular}
                                               \right.\!\!\!\!,
                                                \nonumber\\
                                                \hspace{-6mm}
E_{3}^{-} \!\!\!\!&=&\!\!\!\! \frac{N}{2}\left(3J - 2H - 6\mu\right);
\\[1mm]
\hspace{-6mm}
\label{eq:S_3chiral-}
|{\rm \widetilde{S}}_{3}^{-}\rangle \!\!\!\!&=&\!\!\!\! \prod_{k=1}^N|{\rm \widetilde{S}}_{3}^{-}\rangle_k =
\prod_{k=1}^N\left\{ \!\!\begin{tabular}{l}
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=-\frac{1}{2}\rangle_{L, R}$
                                                            \\[1mm]
                                                            $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=3,S_{k}^{z}=\frac{1}{2}\rangle_{ L, R}$
                                                     \end{tabular}
                                               \right.\hspace{-3mm},\,H \geq 0,
                                                \nonumber\\
                                                \hspace{-6mm}
\widetilde{E}_{3}^{-} \!\!\!\!&=&\!\!\!\! \frac{N}{2}\left(J - 6\mu - 6t\right).
\end{eqnarray}
In above, the superscript 'minus' is again a result of the product ${\rm sgn}(S_k^z)\cdot{\rm sgn}(\sigma_k^z)$.

The ground-state diagram in the $\mu-H$ plane can have several topologies in dependence on the hopping parameter (see~Fig.~\ref{fig:3}). As can be found from Fig.~\ref{fig:3}a, the zero-temperature $\mu-H$ plane includes solely non-chiral phases, namely S$_0$, S$_1^{+}$, S$_3^{+}$, S$_5^{+}$, S$_6$, which have already been observed in the ferromagnetic counterpart of the model, and three new S$_b^{-}$, S$_3^{-}$ if $t/|J|<1/3$. It is clear from Eqs.~(\ref{eq:S_1,5-}), (\ref{eq:S_3-}) that the latter group of phases are characterized by  opposite signs of the total spins of electron plaquettes and the Ising spin states. Moreover, the phases S$_b^{-}$, which appear in the low-field region $H/|J|<1$, remain two-fold degenerate in the whole parameter space. By contrast, the two-fold degeneracy of the phase S$_3^{-}$ is completely canceled as soon as the magnetic field is switched on. If the reverse condition $t/|J|>1/3$ holds, two other non-chiral phases S$_2$, S$_4$ and two chiral phases ${\rm \widetilde{S}}_3^{-}$, ${\rm \widetilde{S}}_3^{+}$ may be observed in the $\mu-H$ plane. The effect of the hopping parameter on the evolution of all four phases can be understood from Figs.~\ref{fig:3}b--e. Obviously, stability regions of the non-chiral phases S$_2$, S$_4$, which can also be found for the ferromagnetic spin-electron interaction $J>0$, are gradually growing at the expense of the phase S$_3^{-}$ when $t$ becomes stronger. The novel chiral phase ${\rm \widetilde{S}}_3^{-}$ emerges merely between the phases S$_2$, S$_4$ in the weak-field region for $1/3<t/|J|<1/2$. If $1/3<t/|J|<2/5$, the horizontal field-induced phase transition ${\rm \widetilde{S}}_3^{-}$--S$_3^{-}$ is gradually shorten and shifted towards higher (but still very weak) magnetic fields with the increasing kinetic term until it completely disappears at $t/|J|=2/5$. If the value of the parameter $t$ further increases, a new horizontal phase boundary S$_2$--S$_4$ emerges along the line $\mu=0$. As a consequence, the phase ${\rm \widetilde{S}}_3^{-}$ completely disappears from the ground-state phase diagram after exceeding the value $t/|J| = 1/2$. Further strengthening of the hopping parameter, which prefers an antiparallel orientation of mobile electrons and the jumping of these particles between individual plaquette sites, leads to the suppression of the interaction $J<0$. As a result, the non-chiral phase S$_3^{-}$, in which electron plaquettes are fully polarized into the magnetic-field direction and the Ising spins are in opposite orientation with respect to the nearest-neighboring electrons, transforms to the chiral one~${\rm \widetilde{S}}_3^{+}$ at $t/|J| = 2/3$. In fact, the phase ${\rm \widetilde{S}}_3^{+}$ is energetically more favorable than S$_3^{-}$ for any values $t/|J|>2/3$ (see Fig.~\ref{fig:3}e).

Regarding to the macroscopic degeneracy of the system, this phenomenon can be identified in the chiral phases ${\rm \widetilde{S}}_3^{+}$, ${\rm \widetilde{S}}_3^{-}$, the non-chiral phases S$_a$ if the magnetic field is zero, and also at some first-order phase transitions.
It is clear from Eqs.~(\ref{eq:S_3chiral+}), (\ref{eq:S_3chiral-}), that the common feature of the first two phases ${\rm \widetilde{S}}_3^{+}$, ${\rm \widetilde{S}}_3^{-}$ is the field-independent two-fold degeneracy of each electron plaquette due to two possible values of the scalar chirality, which leads to the macroscopic degeneracy proportional to $2^N$. Moreover, the phase ${\rm \widetilde{S}}_3^{-}$ is two-fold degenerate in the whole parameter space with respect to two possible spin-electron configurations with opposite signs of $S_k^z$ and $\sigma_k^z$.  As a result, the field-independent macroscopic degeneracy of the phase ${\rm \widetilde{S}}_3^{-}$ is a little bit higher compared to the one of ${\rm \widetilde{S}}_3^{+}$;  one can find ${\cal W} = 2^{N+1}$ in ${\rm \widetilde{S}}_3^{-}$ and  ${\cal W} = 2^{N}$ in ${\rm \widetilde{S}}_3^{+}$. According to the ground-state analysis, the macroscopic degeneracy ${\cal W} = 2^{N+1}$ appears in the zero-temperature $\mu-H$ plane for the hopping parameters $1/3<t/|J|<1/2$, while the macroscopic degeneracy ${\cal W} = 2^{N}$ can be observed for $t/|J|>2/3$. It is worthy to recall that the macroscopic degeneracy of the size ${\cal W} = 2^{N}$ can also be detected in the zero-field region if the phases S$_a$ constitute the ground state. However, this degeneracy is completely canceled by the applied magnetic field, because it comes from the kinetically-driven frustration of the Ising spins [see Eq.~(\ref{eq:S_0,2,4,6})].

Last but not least, the model with the spin-electron interaction $J<0$ is  macroscopically degenerate also at most first-order phase transitions. One can conclude from Fig.~\ref{fig:3} that degeneracy degrees are equal to those observed for the ferromagnetic counterpart of the model: the set of phase transitions S$_p^{\alpha}$--S$_{p\pm1}$ ($\alpha =\{\pm\}$), S$_2$--S$_4$, S$_3^{-}$--S$_3^{+}$ (blue solid  lines) is associated with the degeneracy ${\cal W} = 2^N$, the boundaries separating the chiral phases ${\rm \widetilde{S}^{\alpha}}_{3}$ from the non-chiral ones S$_{3}^{\alpha}$, S$_{2}$, S$_{4}$ (red dashed lines) have the degeneracy ${\cal W} = 3^N$, and finally, the phase transitions S$_q^{\alpha}$--S$_{q+2}^{\alpha}$ (green dot-dashed lines) exhibit the degeneracy ${\cal W} = 4^N$. Note that the macroscopic degeneracy observed at boundaries between the phases S$_q^{\alpha}$, S$_{q+2}^{\alpha}$ is caused by a mutual coexistence of the elementary-unit configurations peculiar to neighboring phases with the chiral ones, namely ${\rm \widetilde{S}}_{(q+1)k}^{+}$ given by Eq.~(\ref{eq:S_2,4chiral+}) (in S$_q^{+}$--S$_{q+2}^{+}$) or ${\rm \widetilde{S}}_{(q+1)k}^{-}$ (in \mbox{S$_q^{+}$--S$_{q+2}^{+}$}). The latter chiral configurations of the elementary unit cell are given by
\begin{eqnarray}
\label{eq:S_2,4chiral-}
|{\rm \widetilde{S}}_{q+1}^{-}\rangle_{k} \!\!\!\!&=&\!\!\!\! \left\{ \begin{tabular}{l}
                                                            $|\!\uparrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=q+1,S_{k}^{z}=-1\rangle_{L, R}$,\,\,\,
                                                            $H = 0$
                                                            \\[1mm]  $|\!\downarrow\rangle_{\sigma_k}$ $\!\otimes$
                                                            $|n_{k}=q+1,S_{k}^{z}=1\rangle_{ L, R}$\hspace{2mm},\hspace{2mm}\,$H \geq 0$
                                                     \end{tabular}
                                               \right.\!\!\!\!,
                                                \nonumber\\
\widetilde{E}_{(q+1)k}^{-} \!\!\!\!&=&\!\!\!\! J -\frac{H}{2} - (q+1)\mu  - t.
\end{eqnarray}
For completeness, it is also necessary to describe a degeneracy of not yet mentioned phase transitions S$_3^{-}$--S$_a$ and S$_3^{-}$--S$_b^{+}$, which are marked as dotted lines in Fig.~\ref{fig:3}. The investigated model is two-fold degenerate at each point of these transitions, because only one localized Ising spin in the model is free to flip, while spin states of the other ones are uniquely determined by mutual interplay between the parameters $J<0$,~$H>0$. It should be noted that the two-fold degeneracy of the first-order phase transitions has not been observed in the ground state of the model with the ferromagnetic spin-electron coupling~$J>0$.
\begin{figure*}[t!]
\centering
\vspace{0.25cm}
\includegraphics[width = 1.0\textwidth]{figure3.eps}
\vspace{-0.5cm}
\caption{\small (Color online) Ground-state phase diagrams of the model with the antiferromagnetic spin-electron interaction $J<0$ constructed in the $\mu-H$ plane for five representative values of the hopping parameter. The black dotted lines denote first-order phase transitions, where the system is two-fold degenerate, while blue solid, red dashed and green dot-dashed lines label first-order phase transitions with the macroscopic degeneracies ${\cal W} = 2^N$, $3^N$ and $4^N$, respectively.}
\label{fig:3}
\end{figure*}

\section{Low-temperature thermodynamics}
\label{sec:4}

The macroscopic ground-state degeneracy may manifest itself in the low-temperature behavior of basic thermodynamic quantities such as entropy and specific heat. The entropy per elementary unit cell in relevant ground-state phase transitions can be directly determined from the degeneracy of the ground-state manifold according to the formula ${\cal S} = k_{\rm B}\!\lim\limits_{N\to\infty}N^{-1}\ln{\cal W}$~\cite{Der04}. Bearing in mind the results presented in Sec.~\ref{sec:3}, the residual entropy per unit cell may take three finite values at the boundaries between different ground states: ${\cal S} = k_{\rm B}\!\ln 2\approx0.693k_{\rm B}$ at S$_2$--S$_4$, S$_3^{-}$--S$_3^{+}$, S$_p^{\alpha}$--S$_{p\pm1}$, ${\cal S} = k_{\rm B}\!\ln 3\approx1.099k_{\rm B}$ at ${\rm \widetilde{S}^{\alpha}}_{3}$--S$_{3}^{\alpha}$, \mbox{${\rm \widetilde{S}^{\alpha}}_{3}$--S$_{2}$,} ${\rm \widetilde{S}^{\alpha}}_{3}$--S$_{4}$, and ${\cal S} = k_{\rm B}\!\ln 4\approx1.386k_{\rm B}$ at S$_q^{\alpha}$--S$_{q+2}^{\alpha}$ (recall that $p=\{1, 5\}$, $q=\{1, 3\}$ and $\alpha =\{\pm\}$). An exception is the group of phase transitions S$_3^{-}$--S$_a$, S$_3^{-}$--S$_b^{+}$ observed in the ground state of the model with the spin-electron coupling $J<0$ (see Fig.~\ref{fig:3}). The entropy of the system takes the finite value $\ln 2$ at each point of these phase transitions due to its two-fold degeneracy caused by one free Ising spin. However, this contribution vanishes in the thermodynamic limit $N\to\infty$. Consequently, the entropy normalized per unit cell takes the value ${\cal S} = 0$, which clearly implies that the model is not macroscopically degenerate at the phase transitions S$_3^{-}$--S$_a$, S$_3^{-}$--S$_b^{+}$. The afore-mentioned statements can be independently checked by low-temperature variations of the entropy depicted in Fig.~\ref{fig:4}. We note that the plotted curves have been obtained from the thermodynamic relation ${\cal S} = -\left(\partial \Omega/\partial T\right)_{H, J, \mu}$~\cite{Hua63}. As one sees in Fig.~\ref{fig:4}, the low-temperature entropy as a function of the chemical potential exhibits a series of narrow peaks at the values corresponding to the relevant ground-state phase transitions, excepting to those that are associated with the phase boundaries S$_3^{-}$--S$_a$, S$_3^{-}$--S$_b^{+}$. The magnitudes of observed peaks are in accordance with the previously reported values of the residual entropy normalized per unit cell. Moreover, two plateaux at ${\cal S} = k_{\rm B}\!\ln 2$ can be identified for the combinations of model parameters $t/J=0.6$, $H/J=0.5$ (if $J>0$) and $t/|J|=0.43$, $H/|J|=0.1$ (if $J<0$) between peaks of the heights ${\cal S} = k_{\rm B}\!\ln 3$ (see Figs.~\ref{fig:4}a, c).
\begin{figure*}[t!]
\centering
\vspace{0.25cm}
\includegraphics[width = 1.0\textwidth]{figure4.eps}
\vspace{-0.5cm}
\caption{\small (Color online) The entropy per elementary unit cell as a function of the chemical potential for the model with the ferromagnetic (figure~a) as well as the antiferromagnetic  (figures~b, c) spin-electron interaction $J$ and several chosen combinations of the parameters $t$, $H$. The~temperature is fixed to the value $k_{\rm B}T/J = k_{\rm B}T/|J| = 0.01$.}
\label{fig:4}
\end{figure*}
Referring to the phase diagrams plotted in Figs.~\ref{fig:2}c and~\ref{fig:3}c one can conclude that these plateaux correspond to the macroscopically degenerate chiral phases ${\rm \widetilde{S}^{+}}_{3}$ and ${\rm \widetilde{S}^{-}}_{3}$, respectively.

The solution for the grand-canonical potential~(\ref{eq:Omega}) allows one to exactly examine the degeneracy of the model also in terms of low-temperature variations of the specific heat. This physical quantity can be obtained by using the relation \mbox{${\cal C} = -T(\partial^{2} \Omega/\partial T^{2})_{H, J, \mu}$~\cite{Hua63}.}

Figure~\ref{fig:5} illustrates the effect of the external magnetic field on temperature dependencies of the specific heat when the ground state is constituted by the phases of different degeneracies. As one sees from Fig.~\ref{fig:5}a, if the zero-field ground state is macroscopically degenerate due to frustration of the Ising spins, the standard single-peak structure of the specific observed for $H=0$ changes to the double-peak one at relatively weak fields. The formation of an additional Schottky-type maximum in the low-temperature part of ${\cal C}(T)$ curve can be attributed to Zeeman splitting of energy levels of the frustrated Ising spins. In accordance with this statement, the field-induced low-temperature maximum gradually shifts towards higher temperatures with the increasing $H$ until it merges with the high-temperature maximum. For two-fold degeneracy that disappears at $H>0$, the zero-field ${\cal C}(T)$ curve may have two-peak or irregular single-peak structure depending on whether total spins of electron plaquettes are $S_k^z = \pm1/2$ or $S_k^z = \pm3/2$, respectively. In the former case, the increasing external field causes a gradual rise of the low-temperature peak and its shifting towards higher temperatures until it completely coalesces with the high-temperature maximum (see Fig.~\ref{fig:5}b). The field evolution of the irregular single-peak structure corresponding to $S_k^z = \pm3/2$ is different. It firstly changes to the two-peak structure at very weak magnetic fields. However, a few significant low-temperature peak very quickly merge with the high-temperature maximum with further increase of $H$ (see Fig.~\ref{fig:5}c). Finally, if two-fold and macroscopic degeneracies of the ground state are maintained at finite magnetic fields, as it is in the phases S$_{b}^{-}$, ${\rm \widetilde{S}}_3^{\alpha}$, two pronounced Shottky-type maxima can be identified in  temperature dependencies of the zero-field specific heat (see Figs.~\ref{fig:5}d, e). In accordance with general expectations, the observed double-peak structure does not significantly change with the increasing magnetic field if one considers parameter combination sufficiently far from phase boundaries.

The interesting multiple-peak dependencies of the specific heat appear also in a proximity of the first-order phase transitions. Typical temperature variations of the quantity ${\cal C}$ corresponding to these regions are illustrated in Fig.~\ref{fig:6}.
If the set of model parameters is chosen to be close enough to boundaries that separate two ground-state phases with unique spin-electron arrangement, ${\cal C}(T)$ curve exhibits one broad Schottky-type maximum in a high-temperature region and one low-temperature Schottky-type maximum regardless of the degeneration degree of the respective phase transition (see Fig.~\ref{fig:6}a). The additional low-temperature peak originates due to thermal excitations between the ground-state configuration and the low-lying excited state with particle configuration of the neighboring phase. A~qualitatively similar temperature variation of the specific heat can also be seen in a proximity of the phase transitions between ground state with the unique particle arrangement and two-fold degenerate ground state (see green dot-dashed curve in Fig.~\ref{fig:6}b).
However, if model parameters are from a neighborhood of the transition between the uniquely ordered and macroscopically degenerate chiral phases, one observes an interesting ${\cal C}(T)$ curve with three Shottky-type peaks (see red dashed curve in Fig.~\ref{fig:6}b).
The maximum at high temperatures involves thermal excitations of diverse physical origin, while the other one located at moderate temperatures originates due to a large number of low-lying excited states that arise out from the chiral phase. Recall that both these peaks have already been identified in $C(T)$ curves corresponding to the chiral ground state ${\rm \widetilde{S}}_3^+$ (see Fig.~\ref{fig:5}e). The third novel peak, which emerges at the lowest temperatures, is a result of thermally induced excitations between particle configurations of the neighboring ground states.
\begin{figure*}[t!]
\centering
\vspace{0.25cm}
\includegraphics[width = 1.0\textwidth]{figure5.eps}
\vspace{-0.5cm}
\caption{\small (Color online) The field evolution of the specific heat versus temperature if the zero-field ground state is constituted by the phase S$_0$ (figure~a), the phases S$_1^{+}$ (figure~b), S$_3^{+}$ (figure~c), S$_1^{-}$ (figure~d), and if the chiral phase ${\rm \widetilde{S}}_{3}^{+}$ is stable the ground state~(figure~e).}
\label{fig:5}
\end{figure*}
\begin{figure*}[t!]
\centering
\vspace{0.25cm}
\includegraphics[width = 1.0\textwidth]{figure6.eps}
\vspace{-0.5cm}
\caption{\small (Color online) Typical temperature dependencies of the specific heat of the model with the antiferromagnetic spin-electron interaction $J<0$ for the combinations of model parameters from a proximity of the first-order phase transitions S$_0$--S$_3^{-}$ (black dotted curve), S$_0$--S$_1^{+}$ (blue solid curve), S$_1^{+}$--S$_3^{+}$ (green dot-dashed curve) (figure~a), S$_1^{-}$--S$_3^{-}$ (green dot-dashed curve), ${\rm \widetilde{S}}_1^{+}$--S$_3^{+}$ (red dashed curve) (figure~b), and if the phases S$_0$ (blue solid curve), S$_4$ (red dashed curve) constitute the zero-field ground state (figure~c).}
\label{fig:6}
\end{figure*}
A remarkable triple-peak temperature dependencies of the specific heat can also be expected in a proximity of the phase transitions S$_a$--S$_b^{-}$, S$_2$--${\rm \widetilde{S}}_3^{\alpha}$, S$_4$--${\rm \widetilde{S}}_3^{\alpha}$ if the phases S$_a$ constitute the ground state and the external magnetic field is very weak, as is demonstrated in Fig.~\ref{fig:6}c. In this case, the moderate peak emerging between two others is associated with low-lying excited states that may be either two-fold or macroscopically degenerate depending on whether they arise out from S$_b^{-}$ or $\widetilde{S}_3^{\alpha}$ ground states, respectively. On the other hand, the origin of the maximum emerging at the lowest temperatures lies in the field-induced splitting of energy levels of the frustrated Ising spins, which can be observed in the phases S$_a$ at $H=0$.

\section{Concluding remarks}
\label{sec:5}

The present paper deals with the exactly solvable double-tetrahedral chain of the localized Ising spins and mobile electrons. Assuming the equal magnetic field acting on all particles, possible ground-state configurations have been particularly discussed for ferromagnetic and antiferromagnetic exchange interactions between mobile electrons and their nearest Ising neighbors. Moreover, thermodynamic quantities such as entropy and specific heat have been calculated by using the exact analytical solution for the grand-canonical potential in order to gain a deeper insight into the degeneracy of individual ground-state phases and phase transitions.

It has been shown that the zero-temperature phase diagram of the model may involve several non-degenerate, two-fold degenerate and macroscopically degenerate chiral phases as a result of mutual interplay between model parameters and the external magnetic field. It has been also demonstrated that the macroscopic degeneracy arising from chiral degrees of freedom of mobile electrons is not canceled by the external magnetic field in contrast to the macroscopic degeneracy appearing due to a frustration of the localized Ising spins. Both these degeneracies are manifested themselves in the same residual entropy per elementary unit cell ${\cal S}=k_{\rm B}\ln 2$ and can be detected in the ground state of the model regardless of the nature (sign) of the spin-electron interaction. On the other hand, the field-independent two-fold degeneracy can be observed at $T=0$ only for the antiferromagnetic spin-electron interaction if triangular plaquettes are occupied by one or five mobile electrons and the total spin of the electron plaquette and the spin state of its Ising neighbor have opposite signs. A diversity of the ground-state degeneracy appearing in individual first-order phase transitions has been confirmed by low-temperature dependencies of the entropy. Finally, the effect of the ground-state degeneracy and the applied magnetic field on temperature dependence of the specific heat has been examined in detail. It has been evidenced that the mutual interplay of all factors may lead to complex temperature dependencies of the specific heat with two or three Schottky-type maxima.

\section*{Acknowledgments}
The work was financially supported by the grant No.~APVV-0097-12 of the Slovak Research and Development Agency under the contract and by the scientific grant VEGA 1/0043/16 of The Ministry of Education, Science, Research and Sport of the Slovak Republic.
Special thanks belongs to long-time collaborator Jozef Stre\v{c}ka for his valuable comments on this work.

\section*{References}

redpajama_set_name: RedPajamaArXiv


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There are several reasons why Bingo has been popular with UK players. First of all, it is a simple game with easy to learn rules. Stakes are low and all you have to do is to pick your lucky numbers. With Lady Luck by your side, you can win a jackpot worth hundreds or thousands of pounds. Bingo is not a solitary activity like other forms of entertainment. If you play it at a Bingo hall, you can meet other players and make friends with them. When playing it online, you can join Bingo rooms where you can chat with fellow players and make friends as well.
On the web, you can find a plethora of dedicated Bingo sites where you can try your luck without leaving the comfort of your home. They are optimized for mobile play thus allowing you to take your favourite game wherever you go. If you like to play a few rounds while commuting, no problem! Just login into your account via your smartphone or tablet and you can play Bingo as long as your internet connection is stable.
While some sites allow you to play Bingo in the free-play mode, wagering real money provides you with a chance to win real money jackpots. That adds more excitement to the gameplay. Yet, when risking your own money, you want to be sure that the Bingo site you make your deposits to will treat you fairly and that your funds will be safe. That's why it is of the utmost importance to sign up only with the websites that are fully licensed and regulated. A gaming licence ensures that the gaming establishment uses a Random Number Generator (RNG) that produces fair and unbiased results in bingo ball draws.
Another thing you should consider when choosing a Bingo site is a range of games it offers. While online casinos have a number of Bingo games on offer, dedicated sites offer much more. You can play 90-ball bingo, which is the most popular version of the game in the UK, but the games using 75, 50 and 30 balls are also available. You may want to know more about software providers as the overall quality of your gaming experience depends on that. Not all developers provide players with the same level of quality, so look out for websites powered by some of the biggest names in the industry such as Dragonfish, Gamesys or Cozy Games.
The origin of Bingo is not known precisely. Some believe it stemmed from Italian lottery while others think that its roots are in 19th-century educational game used in Germany to teach children how to spell and count. At the beginning of the 20th century, Bingo was popular with US citizens who played it during carnivals. Back then, Bingo was played with beans and called Beano until one of the players mispronounced "Beano!", which was used when someone won a game. That's how the game got its name.
When it comes to the UK, it is believed that Bingo was firstly introduced in the 18th century. Today, you can play the game in Bingo halls and online on dedicated websites. Since it is played with real money, it is considered a form of gambling. In the UK, Bingo gaming venues are regulated by the UK Gambling Commission. The trustworthy gaming authority protects UK citizens as long s they play in licensed gaming establishments, offline or online.
This game is a part of the tradition in the UK and it is fun to play. Since its rules are simple, you can start playing Bingo in no time. The great news is that today you can choose whether you will play Bingo at a brick-and-mortar hall, online or even on the go. Whichever option that you prefer, make sure to play the game of Bingo in a gaming venue holding a proper UK Gambling Commission gaming licence.


One of the reasons I was keen to renew my Ancestry membership was because the organisation has just released a new collection of Masters and Mates certificates for Great Britain from 1850-1927, as sourced from The National Maritime Museum at Greenwich.
Some years ago I went to London to seek out the Register entries for my CUMPSTON relatives who were all Master Mariners. I was able to abstract all their register of sailing entries, including ships and dates. but never got to see their actual certificates – so what joy this evening to be able to download them. I found 2 certificates for my 2 x great grandfather Watson CUMPSTON – the first certificate showed him aged 24 born in 1833 in Hull, with a certificate of competency as 'Only Mate' dated 30th October 1857. The second dated 1861 was as a 'Master'.
and Thomas Cumpston dated 1851 – a beautiful Mate's certificate showing that he had worked for 25 years in the British Merchant Service in the 'Foreign Trade'.
The collection is available at http://search.ancestry.co.uk/search/db.aspx?dbid=2271.
Do let me know if you are related to any of these people.
This entry was posted in Cumpston people, Research resources and tagged Charles West Cumpston, Cumpston, Greenwich, Kingston upon Hull, National Maritime Museum, Watson Cumpston. Bookmark the permalink.