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

In recent years frustrated quantum spin systems on regular two-dimensional
(2D) lattices  have aroused a great deal of research interest.
\cite{2D_magnetism_1,2D_magnetism_2,2D_magnetism_3}  In particular the
interplay of magnetic frustration and quantum fluctuations has been
seen to be a very effective route to destabilize or destroy
magnetic order and thereby to create new quantum phases.
Such 2D magnetic systems can thus in turn develop a diverse array of phases with
widely different ordering properties, such as antiferromagnets with quasiclassical N\'eel
ordering, quantum ``spirals'', valence-bond
crystals/solids, phases with nematic ordering, and spin liquids.  Other factors that
influence the ground-state (gs) phase structures are the nature of the
underlying crystallographic lattice, the number and nature of the bonds on
this lattice, and the spin quantum numbers of the atoms localized to
the sites on the lattice.  The theoretical investigation of these
models has proceeded hand in hand with the discovery and experimental
investigation of ever more quasi-2D magnetic materials with novel properties.

One of the most intensively studied of all of the frustrated 2D models is the
spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ Heisenberg antiferromagnet (HAF)  on the square lattice with
nearest-neighbor (NN) bonds (of strength $J_{1} > 0$) competing with
next-nearest-neighbor (NNN) bonds (of strength $J_{2} \equiv \alpha
J_{1} > 0$). This quantum system has two different quasiclassical phases with collinear
magnetic long-range order (LRO) at small ($\alpha < \alpha_{c_{1}}
\approx 0.4$) and large ($\alpha > \alpha_{c_{2}} \approx 0.6$) values
of the frustration strength parameter $\alpha$,
separated by an intermediate quantum paramagnetic phase
with no magnetic LRO in the regime $\alpha_{c_{1}} < \alpha <
\alpha_{c_{2}}$.  Interest in this model has been greatly stimulated recently
by its experimental realization in such layered magnetic materials as
Li$_2$VOSiO$_4$,\cite{Mel:2000,Ro:2002}
Li$_2$VOGeO$_4$,\cite{Mel:2000} and VOMoO$_4$.\cite{Bom:2005}  The syntheses of such layered
quasi-2D materials has stirred up a great deal of renewed interest in
the model (and see also, e.g.,
Refs.~[\onlinecite{Ca:2000,Ca:2001,Sin:2003,Ro:2004}]).  Amongst
several methods that have been very successfully applied to
the $J_{1}$--$J_{2}$ model has been the coupled cluster method
(CCM),\cite{j1j2_square_ccm1,Bi:2008_PRB,Bi:2008_JPCM,j1j2_square_ccm5} which
has also been applied to many similar strongly-interacting and
highly frustrated spin-lattice models with comparable success.
Other frustrated 2D models that have similarly engendered great recent
interest include the spin-$\frac{1}{2}$ HAFs
on the triangular\cite{Bernu:1994,Zeng:1995} and kagome
lattices.\cite{Kagome_Schn:2008,Eve:2010}

There has been a large amount of recent experimental investigation
of the properties of quasi-2D magnetic materials with a
ferromagnetic (FM) NN coupling ($J_{1}<0$) and an antiferromagnetic
(AFM) NNN coupling ($J_{2} > 0$).  Examples include
Pb$_{2}$VO(PO$_{4}$)$_{2}$,\cite{Kaul:2004,Skoulatos:2007,Carretta:2009,Skoulatos:2009,Nath:2009}
(CuCl)LaNb$_{2}$O$_{7}$,\cite{Kageyama:2005}
SrZnVO(PO$_{4}$)$_{2}$,\cite{Skoulatos:2009,Tsirlin:2009_PRB79,Tsirlin:2009_PRB80}
BaCdVO(PO$_{4}$)$_{2}$,\cite{Carretta:2009,Tsirlin:2009_PRB79,Nath:2008}
PbZnVO(PO$_{4}$)$_{2}$,\cite{Tsirlin:2010} and
(CuBr)LaNb$_2$O$_7$.\cite{oba2006}  These experimental studies have also served to
reignite interest in the theoretical investigation of the
gs and thermodynamic properties of the FM
$J_{1}$--$J_{2}$ model, i.e., the model with FM NN exchange ($J_{1}<0$)
and frustrating AFM NNN exchange ($J_{2}>0$).{\cite{shannon04,shannon06,sindz07,schmidt07,schmidt07_2,sousa,
shannon09,sindz09,haertel10,Richter:2010,sousa2011,momoi2011}
Interestingly, arguments for the existence of a spin-nematic phase between
two quasiclassical magnetically-ordered phases were
presented.\cite{shannon06,shannon09,sindz09,momoi2011} On the other hand, the
existence of such a non-classical magnetically-disordered phase was also
questioned in Ref.~[\onlinecite{Richter:2010}].

Other systems that have grown in importance in the last few years are
various spin-$\frac{1}{2}$ magnetic models defined on the 2D honeycomb lattice.
Several such systems have been both theoretically and experimentally studied
\cite{wang2010,honey1,honey2,honey3,honey5,schmidt2011,lauchli2011,honey7,oitmaa2011,exp}
intensively, partly because of their special properties and partly due to
the recent syntheses of various quasi-2D honeycomb-lattice materials.
One reason for the theoretical interest in such models on the 2D honeycomb lattice is that a
spin-liquid phase has been found for the exactly solvable Kitaev
model,\cite{kitaev} in which the spin-$\frac{1}{2}$ particles reside
on just such a lattice.  Furthermore, the honeycomb lattice is obviously germane to
the very active research field of graphene, where the relevant physics
may well be described by Hubbard-like models on this
lattice.\cite{graphene,meng,schmidt2011} Interestingly, Meng {\it
  et al.}\cite{meng} found that for the Hubbard model on the honeycomb
lattice with moderate values of the Coulomb repulsion parameter $U$, strong
quantum fluctuations lead to an insulating spin-liquid phase
between the non-magnetic metallic phase and the AFM Mott insulator phase.
From the experimental side recent observations on the
spin-$\frac{3}{2}$ honeycomb-lattice HAF Bi$_3$Mn$_4$O$_{12}$(NO$_3$)
demonstrate a spin-liquid-like behavior at temperatures much lower
than the Curie-Weiss temperature.\cite{exp}

We have recently studied\cite{DJJF:2011_honeycomb} the AFM $J_{1}$--$J_{2}$--$J_{3}$
honeycomb model for the case where the spin quantum number $s$ of each
of the spins on every lattice site is $s=\frac{1}{2}$, and with
AFM nearest-neighbor exchange bonds ($J_{1}>0$) in the presence of
frustration caused by AFM NNN bonds ($J_{2}>0$) and with
next-next-nearest neighbor (NNNN) bonds of strength $J_{3}$ also present,
for the special case where $J_{3}=J_{2}$. We found\cite{DJJF:2011_honeycomb}
that the scenario of deconfined criticality may hold for this model
(and see also Ref.~[\onlinecite{lauchli2011}]).
To date there exist only limited studies of the corresponding
FM $J_{1}$--$J_{2}$--$J_{3}$ model (namely where $J_{1}<0$).  In this paper, we further the
investigation into the FM $J_{1}$--$J_{2}$--$J_{3}$
honeycomb model with FM NN bonds (of strength $J_{1}<0$) in the presence of frustrating
AFM NNN bonds (of strength $J_{2}>0$) and NNNN bonds (of strength $J_{3} > 0$).
Once again we consider only the interesting special case where $J_{3}=J_{2}$.
We focus our attention in the present study particularly on the
detection and characterization of the gs phases of the
quantum model. Bearing in mind the controversial discussion of the
corresponding $J_{1}$--$J_{2}$ square-lattice  model with FM NN
exchange bonds ($J_{1}<0$),  the question naturally arises
as to whether any indications for  a non-classical
magnetically-disordered phase might now be found for the honeycomb model.
To determine the relevant gs phases and their properties we
calculate the gs energy, the spin-spin correlation function, and the magnetic order
parameter for the stripe-ordered state discussed below that is present
as a gs phase in the corresponding
classical version (equivalent to the $s \rightarrow \infty$ limit) of the model.

In view of its proven past ability to give results of high accuracy for a wide
variety of highly frustrated 2D spin-lattice models, we again use
the coupled cluster method (CCM) as our main computational tool
in this paper.  Additionally, we use the exact diagonalization (ED)
method for a large finite lattice of $N=32$ spins as a validity check of our CCM
results.  Since at the classical level the model now under consideration also exhibits
some similarities with the corresponding model with  AFM NN bonds ($J_{1}>0$),
we compare our results for the quantum model of the FM case ($J_{1} \equiv -1$)
with those of the corresponding AFM case ($J_{1} \equiv +1$).

The rest of the paper is organized as follows.  After describing the
model in Sec. \ref{model_section}, we apply the CCM to investigate its
gs properties. The CCM itself is very briefly described in
Sec. \ref{CCM}, before presenting and discussing our CCM and ED
results in Sec. \ref{results}.  We conclude in
Sec. \ref{conclusions} with a summary of the main results.

\section{The model}
\label{model_section}
The Hamiltonian of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
Heisenberg model on the honeycomb
lattice, which we studied
recently\cite{DJJF:2011_honeycomb} for the AFM case ($J_{1}>0$) is defined as
\begin{equation}
H = J_{1}\sum_{\langle i,j \rangle} \mathbf{s}_{i}\cdot\mathbf{s}_{j} + J_{2}\sum_{\langle\langle i,k \rangle\rangle} \mathbf{s}_{i}\cdot\mathbf{s}_{k} +
J_{3}\sum_{\langle\langle\langle i,l \rangle\rangle\rangle} \mathbf{s}_{i}\cdot\mathbf{s}_{l}\,,
\label{H}
\end{equation}
where $i$ runs over all lattice sites on the lattice, and where $j$ runs
over all NN sites connected to site $i$ by $J_{1}$ bonds,
$k$ runs over all NNN sites connected to site $i$ by $J_{2}$ bonds, and
$l$ runs over all NNNN sites connected to site $i$ by $J_{3}$ bonds,
but counting each bond once and once only in the three sums.
Each site $i$ of the lattice carries a spin-$\frac{1}{2}$
particle with spin operator ${\bf s}_{i} \equiv (s_{i}^{x},s_{i}^{y},s_{i}^{z})$.
We note that precisely the same model has also been studied recently on the square
lattice, both in the case where all the bonds are AFM in nature,\cite{Reuther:2011_J1J2J3mod}
and in the FM case where $J_{1}<0$ and $J_{2}>0, J_{3}>0$.\cite{Feldner:2011_J1J2J3mod}

The aim of the present work is now to study further the
spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ FM model (namely the above model in the case
$J_{1}<0$) on the honeycomb
lattice.\cite{honey1,honey2,honey3,honey4,honey5}  The lattice and
the exchange bonds are illustrated in Fig.~\ref{model}(a).
\begin{figure*}[!tb]
\mbox{
\subfloat[FM]{\scalebox{0.35}{\includegraphics{fig1a.eps}}}
\qquad
\subfloat[striped AFM]{\scalebox{0.35}{\includegraphics{fig1b.eps}}}
}
\caption{(Color online) The $J_{1}$-$J_{2}$-$J_{3}$ honeycomb model, showing
  (a) the ferromagnetic (FM) state and (b) the classical striped antiferromagnetic (AFM) state.
  The arrows represent spins located on lattice sites \textbullet.}
\label{model}
\end{figure*}
The classical gs phase diagram for the $J_{1}$--$J_{2}$--$J_{3}$
AFM model (with $J_{1}>0$) on the honeycomb lattice model displays
collinear N\'{e}el and striped phases, both AFM in nature, as well as a spiral phase. These
phases meet in a triple point at $J_{3}=J_{2}=J_{1}/2$ (and for more
details see, e.g., Ref.~[\onlinecite{honey3}]).  For the
remainder of this paper we again focus on the case where $J_{3}=J_{2}>0$}, but now where the
NN exchange bond is FM in nature ($J_{1}<0$).  The
gs energies of the only two corresponding classical collinear states are
then given by
\begin{eqnarray}
\frac{E^{\mbox{\tiny{cl}}}_{\mbox{\tiny{FM}}}}{{N}} &=& s^{2} \left (\frac{3}{2}J_{1} + \frac{9}{2}J_{2} \right),\nonumber \\
\frac{E^{\mbox{\tiny{cl}}}_{\mbox{\tiny{striped AFM}}}}{{N}} &=& s^{2} \left (\frac{1}{2}J_{1} - \frac{5}{2}J_{2} \right), \label{H_classical}
 \end{eqnarray}
for the FM state and collinear striped AFM state shown in Figs.~\ref{model}(a) and (b) respectively.
If these were the only gs phases in this $J_{1}<0$ regime we would thus
have a classical transition between the FM state and the striped AFM state at $J^{\rm cl}_{2}=-\frac{1}{7} J_{1}$
($\approx 0.143$ for $J_{1}=-1$) and a classical energy per site at this point of
$E^{\rm cl}/N = -\frac{3}{14} \approx -0.214$ for the $s=\frac{1}{2}$ system with $J_{1}=-1$.
For the corresponding AFM model with $J_{1}>0$ such a  striped AFM
state also exists as stated above, but the classical transition
between the AFM N\'{e}el state and the striped AFM state is at
$J_{2}=+\frac{1}{2}J_{1}$.  The reason why the corresponding phase
transition in the FM model occurs at a smaller value of the frustration
parameter, $J^{\rm cl}_{2}/|J_{1}|=\frac{1}{7}$ than the value
$J^{\rm cl}_{2}/J_{1}=\frac{1}{2}$ for the AFM model is due
to the $J_{3}$($>0$) NNNN exchange bonds that act to frustrate the
fully polarized FM state, whereas they reinforce the AFM N\'eel state.
By contrast, the $J_{2}$($>0$) NNN exchange bonds act to frustrate
the $J_1$ bonds for both the FM state of the FM model and the
N\'eel state of the AFM model.
We note that the classical FM state is also an eigenstate of the Hamiltonian, with
energy eigenvalue equal to the energy of its classical FM counterpart.

We note, however, that in fact the classical $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg model on
the honeycomb lattice with $J_{1}<0$, $J_{2}>0$, and $J_{3}>0$ also has a spiral
phase that intervenes in a very narrow strip between the FM phase and the collinear
striped AFM phase.  (In Refs.~[\onlinecite{honey3,Rastelli:1979}] this is referred to
as phase V.)  The region in the $x$-$y$ plane (where $x \equiv J_{2}/J_{1}$ and $y \equiv J_{3}/J_{1}$)
in which it is the stable gs phase in the case $J_{1}<0$ is bounded by the three
curves (i) $y=0$, $-\frac{1}{2}<x<-\frac{1}{6}$, (ii) $y=-\frac{3}{2}x-\frac{1}{4}$,
$-\frac{1}{6}<x<\frac{1}{2}$, and (iii) $y=\frac{1}{8}[1-6x-\sqrt{36x^2+20x+17}]$,
$-\frac{1}{2}<x<\frac{1}{2}$.  The point $(x=\frac{1}{2},y=-1)$ is a classical
tetracritical point at which the spiral phase V meets the FM phase, the striped
collinear AFM phase, and the AFM N\'eel phase (and see Fig. 3 of
Ref.~[\onlinecite{honey3}] for further details).  Thus, in our case, where
$J_{3}=J_{2}$ and $J_{1}<0$, the classical spiral phase V exists in the
narrow region $\frac{1}{10}<J_{2}/|J_{1}|<\frac{1}{5}$.  Naturally this
includes the point $J^{\rm cl}_{2}/|J_{1}|=\frac{1}{7}$ discussed above
at which the FM and striped collinear AFM phases would meet in the
absence of the spiral phase V as a stable gs phase intervening between them.

In all of our results below for the FM $J_{1}$--$J_{2}$--$J_{3}$
honeycomb
system we henceforth set $J_{1} \equiv -1$
with no loss of generality, since this simply sets the overall scale of the
Hamiltonian, and we consider the case where $J_{3}=J_{2}>0$, such
that both the NNN and NNNN bonds act to frustrate the ferromagnetism.

\section{Coupled Cluster Method}
\label{CCM}
The CCM (see, e.g., Refs.~[\onlinecite{Bi:1991,Ze:1998,Fa:2004}] and
references cited therein) that we use here is one of the most powerful
and most versatile modern techniques in quantum many-body theory.  It
has been used to study various quantum magnets (see, e.g.,
Refs.~[\onlinecite{j1j2_square_ccm1,Bi:2008_PRB,Bi:2008_JPCM,j1j2_square_ccm5,Fa:2001,Kr:2000,
Schm:2006,Fa:2004,Ze:1998,shastry2,shastry3,square_triangle,UJack_ccm,Bi:2010_kagomeSquare,Bi:2011_UJack_greatSpins}]
and references cited therein) very successfully.  The method is
particularly suitable for investigating frustrated systems, due to the
fact that some of the main alternative methods are restricted by
certain problems that arise in such cases.  For instance, quantum Monte Carlo (QMC) techniques
suffer from the infamous and well-known ``sign problem'' for such systems.  The exact
ED method is also usually restricted by available computational
power to relatively small finite-sized lattices.  Nevertheless it
can often be used, as here, to provide a handy tool to
check and validate the results of other numerical or approximate
methods.

We briefly describe here some of the important features of the CCM
as applied to spin-lattice problems (and see, e.g.,
Refs.~[\onlinecite{Ze:1998,Kr:2000,Fa:2001,Schm:2006,j1j2_square_ccm1,Fa:2004}]
and references cited therein for further details).  The starting point for any
CCM calculation is to select a normalized state
$|\Phi\rangle$ as a reference or model state against which to incorporate in a
systematic and potentially exact fashion the correlations present in the
exact ground state.  We often use a relevant classical ground state as the model
state for spin systems for the sake of convenience, but other appropriate states
may certainly also be used.  In order to treat each site
equivalently, a mathematical rotation of the local axes of
the spins is conveniently performed in such a way that all spins in the
reference state align along the same direction, say the
negative $z$-axis.  Clearly, such rotations leave unchanged the SU(2)
commutation relations between components of the spin operators.

The exact ket and bra gs energy eigenstates,
$|\Psi\rangle$ and $\langle\tilde{\Psi}|$, of the many-body system are
then parametrized in the CCM form as: \vskip0.2cm
\begin{equation}
|\Psi\rangle = \mbox{e}^{S}|\Phi\rangle; \qquad S = \sum_{I\neq0}{\cal S}_{I}C^{+}_{I},   \label{eq:ket_eq}
\end{equation}
\begin{equation}
\langle\tilde{\Psi}| = \langle\Phi|\tilde{S}\mbox{e}^{-S}; \qquad \tilde{S} = 1 + \sum_{I\neq0}\tilde{{\cal S}_{I}}C^{-}_{I},   \label{eq:bra_eq}
\end{equation}
where
\begin{equation}
H|\Psi\rangle = E|\Psi\rangle; \qquad \langle\tilde{\Psi}|H = E\langle\tilde{\Psi}|,  \label{eq:SE_CCM}
\end{equation}
are the Schr\"{o}dinger gs ket and bra equations respectively.
The multiconfigurational creation operators $C^{+}_{I} \equiv (C^{-}_{I})^{\dagger}$ are
defined so that $\langle \Phi |C^{+}_{I} = 0 = C^{-}_{I}| \Phi \rangle \;; \forall I \neq 0$, and
where we have defined $C^{+}_{0} \equiv 1 \equiv C^{-}_{0}$.
They are required to form a complete set of mutually commuting many-body creation operators
in the Hilbert space, defined with respect to $|\Phi\rangle$ as a cyclic vector.
Clearly the states are normalized such that $\langle\tilde{\Psi}|\Psi\rangle =
\langle \Phi| \Psi\rangle = \langle \Phi| \Phi \rangle \equiv 1$.
For spin-lattice systems they take the form of multi-spin raising operators and
are written as products of single-spin raising operators, $C^{+}_{I}\equiv s^{+}_{j_{1}}
s^{+}_{j_{2}} \cdots s^{+}_{j_{n}}$, where $s^{+}_{j} \equiv s^{x}_{j} + is^{y}_{j}$.
The gs energy is calculated in terms of the correlation
coefficients $\{{\cal S}_{I}\}$ as $E=\langle\tilde{\Psi}|H|\Psi\rangle =
\langle\Phi|\mbox{e}^{-S}H\mbox{e}^{S}|\Phi\rangle$; and the average on-site
magnetization $M$ in the rotated spin coordinates is calculated
equivalently in terms of the coefficients $\{{\cal S}_{I},\tilde{{\cal S}_{I}}\}$
as $M \equiv -\frac{1}{N} \langle\tilde{\Psi}|\sum_{j=1}^{N}s^{z}_{j}|\Psi\rangle$,
which now plays the role of the order parameter.
Finally, the complete set of unknown ket- and bra-state correlation coefficients
$\{{\cal S}_{I}, \tilde{{\cal S}_{I}}\}$ is calculated by requiring the expectation
value $\bar{H}=\langle\tilde{\Psi}|H|\Psi\rangle$ to be a minimum with
respect to all parameters $\{{\cal S}_{I}, \tilde{{\cal S}_{I}}\;; \forall I \neq 0\}$.
This readily leads to the coupled set of nonlinear equations for the ket-state creation
correlation operators $\{{\cal S}_{I}\}$, $\langle \Phi|C^{-}_{I}\mbox{e}^{-S}H\mbox{e}^{S}|\Phi\rangle =
0\;; \forall I \neq 0$, and to the coupled set of linear equations,
$\langle\Phi|\tilde{S}(\mbox{e}^{-S}H\mbox{e}^{S} - E)C^{+}_{I}|\Phi\rangle = 0\;; \forall I \neq 0$,
which can then be solved for the bra-state destruction correlation operators
$\{\tilde{{\cal S}_{I}}\}$.

When all many-body configurations $\{I\}$ are included in the expansions of the correlation expansions
operators $S$ and $\tilde{S}$, the CCM formalism is exact.  However, it is
necessary of course in practice to use approximation schemes to truncate the
sets of configurations $\{I\}$ contained in the expansions of
Eqs. (\ref{eq:ket_eq}) and (\ref{eq:bra_eq}) for the CCM
correlation operators.  For systems defined on a regular periodic
spatial lattice as here, it is convenient to use the well-established
LSUB$m$ approximation scheme in which all possible multi-spin-flip
correlations over different locales on the (here, honeycomb) lattice defined by
$m$ or few contiguous lattice sites are retained.
Clusters are defined to be contiguous in this sense if every
site in the cluster is adjacent (as a nearest neighbor)
to at least one other site in the cluster.  This is the scheme
we use for all our results presented below.  The number $N_{f}$ of
independent fundamental clusters (i.e., those that are inequivalent
under the symmetries of the Hamiltonian and of the model state)
increases rapidly with the truncation index $m$, as shown in
Table~\ref{table_FundConfig}
\begin{table}
  \caption{Number of fundamental LSUB$m$ configurations ($N_{f}$) for the collinear
   striped AFM state of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ honeycomb model.}
\label{table_FundConfig}
\begin{tabular}{cc} \hline\hline
{Method} & {$N_{f}$} \\
\hline
LSUB6 & 72    \\
LSUB8 & 941   \\
LSUB10 & 14679 \\
LSUB12 & 250891 \\ \hline\hline
\end{tabular}
\end{table}
for the present spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
model on the honeycomb lattice, where we use the natural lattice geometry
itself to define the notion of adjacency inherent in the definition
of the LSUB$m$ scheme.  We see, for example, that the
number $N_{f}$ of such fundamental clusters (and hence the number of simultaneous nonlinear
equations we need to solve for the retained correlation coefficients
$\{{\cal S}_{I}\}$) for the striped model state is 250891 at the highest LSUB12 level of
approximation that we utilize here.  The corresponding numbers, $N_f$, of
fundamental configurations are appreciably higher at a given LSUB$m$ level
when the spiral phase V is used as the CCM model state, due to the considerably
reduced symmetry.  It is necessary to use
massive parallelization and supercomputing resources in order to
perform the CCM calculations at such high level of approximation.\cite{ccm}  Thus, for
example, to obtain a single data point (i.e., for a given value of $J_{3}=J_{2}$) for
the striped model state at the LSUB12 level typically requires about 0.5 h
computing time using 1000 processors simultaneously.

We present CCM results below based on the striped collinear AFM state as model state,
at various LSUB$m$ levels of
approximation with $m=\{6,8,10,12\}$, and also in the corresponding $m \rightarrow \infty$
extrapolated limits (LSUB$\infty$) based on the
well-tested extrapolation schemes described below and in more detail
elsewhere.\cite{Ze:1998,Fa:2004,j1j2_square_ccm1,Bi:2008_PRB,Bi:2008_JPCM}
We have also performed extrapolations for the data set with
$m=\{6,8,10\}$.  Both sets of results agree well with
one another, which gives added credence to our results.
Note that we do not use the LSUB$m$ approximation scheme for values $m<6$ of
the truncation index, since these low-order approximations
will not capture the natural hexagonal structure of the lattice.
We remark that, as always, the CCM exactly obeys the
Goldstone linked-cluster theorem at every LSUB$m$ level of
approximation.  Hence we work from the outset in the limit $N
\rightarrow \infty$, where $N$ is the number of sites on the honeycomb
lattice, and extensive quantities such as the gs energy are always
guaranteed to be linearly proportional to $N$ in this limit.

We clearly do not need to perform any finite-size scaling of our results, as all CCM
approximations are automatically performed from the outset in the
infinite-lattice limit, $N \rightarrow \infty$, as discussed above.
It is, however, necessary to extrapolate to
the exact $m \rightarrow \infty$ limit in the LSUB$m$ truncation index
$m$, in which limit the complete (infinite) Hilbert space is reached.  For
the gs energy per spin, $E/N$, a well-tested and very accurate extrapolation
ansatz (and see, e.g., Refs.,
[\onlinecite{Bi:2008_PRB,Bi:2008_JPCM,Richter:2010,Kr:2000,rachid05,ccm3}])
is
\begin{equation}
E(m)/N = a_{0}+a_{1}m^{-2}+a_{2}m^{-4}\,,   \label{E_extrapo}
\end{equation}
while for the magnetic order parameter, $M$, different schemes have been
employed for different situations. For models showing no or only
relatively small amounts of frustration, a well-tested and accurate
rule (and see, e.g., Refs.~[\onlinecite{Kr:2000,rachid05}]) is
\begin{equation}
M(m) = b_{0}+b_{1}m^{-1}+b_{2}m^{-2}\,.    \label{M_extrapo_standard}
\end{equation}
For highly frustrated systems, particularly those showing a gs order-disorder transition, a more appropriate
extrapolation rule with fixed exponents that has been found to give good results (and see, e.g.,
Refs.~[\onlinecite{Bi:2008_PRB,Richter:2010}]) is
\begin{equation}
M(m) = c_{0}+c_{1}m^{-1/2}+b_{2}m^{-3/2}\,.    \label{M_extrapo_frustrated}
\end{equation}
We give illustrations here of the use of each of these schemes, wherever and whenever possible.

\section{Results and Discussion}
\label{results}
We now present and discuss our CCM results.  In order to have an
independent check on the accuracy and consistency of our CCM results,
we have also performed additional computations of selected gs properties of the
present models using the ED technique that is a well-established and
successful tool for studying frustrated quantum spin systems (and see, e.g.,
Refs.~[\onlinecite{Richter:2010,schulz,
waldtmann,ED40,lauchli2011,nakano2011}]).
In Fig.~\ref{E}(a) we show the CCM results for the gs energy per spin, $E/N$, in
various LSUB$m$ approximations based on the striped state as CCM model state,
as well as the exact gs energy for a finite lattice of size $N=32$.
\begin{figure*}[!t]
\begin{center}
\mbox{
  \subfloat[$m=6,8,10,12$]{\scalebox{0.3}{\includegraphics[angle=270]{fig2a.eps}}}
 }
\mbox{
\subfloat[$m \rightarrow \infty$]{\scalebox{0.3}{\includegraphics[angle=270]{fig2b.eps}}}
}
\caption{
  (Color online) Ground-state energy per spin, $E/N$, versus
  $J_{2}$ for the striped phase of the spin-$\frac{1}{2}$
  $J_{1}$--$J_{2}$--$J_{3}$ honeycomb model with $J_{1}=-1$ compared with those for
  $J_{1}=+1$ (with $J_{3}=J_{2}>0$ for both cases).  The CCM results using
  the striped model state for various LSUB$m$ approximations with
  $m=\{6,8,10,12\}$, together with the ED ($N=32$) results are shown in (a).
  We show in (b) the extrapolated CCM LSUB$\infty$ results using the $m=\{6,8,10,12\}$
  data points fitted to Eq. (\ref{E_extrapo}).  In all cases curves without symbols attached
  refer to the case $J_{1}=-1$, whereas the corresponding curves
  with symbols refer to the case $J_{1}=+1$. The FM result
  from Eq. (\ref{H_classical}) with $s=\frac{1}{2}$ is also displayed.
  }
\label{E}
\end{center}
\end{figure*}
We also show separately, in Fig.~\ref{E}(b), the extrapolated ($m \rightarrow \infty$) results
obtained from Eq.~(\ref{E_extrapo}) using the data set
$m=\{6,8,10,12\}$.  Comparison is made with the results for the corresponding
AFM version of the model with $J_{1}=+1$.

The CCM LSUB$m$ data displayed in Fig.~\ref{E}(a) show that the gs energy results
converge extremely rapidly as the truncation index $m$ is increased, such that
the difference between the LSUB12 results and the extrapolated
($m \rightarrow \infty$) results obtained from Eq. (\ref{E_extrapo}) is
very small indeed.  We note too that, just as in the corresponding AFM case of the
model with $J_{1}=+1$, the various CCM LSUB$m$ solutions based on the striped model
state now also terminate at some lower termination point $J^{t}_{2}$ as $J_{2}$ is decreased.
Such terminations of CCM solutions are very common
and have been very well documented.\cite{Fa:2004} In all such cases a termination
point always arises due to the solution of the CCM
equations becoming complex at this point, beyond which
there exist two branches of entirely unphysical complex conjugate
solutions.\cite{Fa:2004}  In the region where the solution reflecting
the true physical solution is real there actually also exists
another (unstable) real solution. However, only the shown
branch of these two solutions reflects the true (stable) physical
ground state, whereas the other branch does not. The
physical branch is usually easily identified in practice as the
one which becomes exact in some known (e.g., perturbative)
limit. This physical branch then meets the corresponding unphysical
branch at some termination point with infinite
slope, beyond which no real solutions exist. The
LSUB$m$ termination points are themselves also reflections of
the quantum phase transitions in the real system and may be
used to estimate the position of the phase boundary,\cite{Fa:2004} although
we do not do so for this critical point in the FM model, since we
have more accurate criteria that we now discuss.

We note first from Fig.~\ref{E}(a) that the LSUB$m$ termination points using
the striped state as the CCM model state for the
present FM version of the model with $J_{1}=-1$, lie very close indeed to
the points where the curves cross (or nearly cross) the corresponding curve
for the FM state given by Eq. (\ref{H_classical}).  This gives us our
first evidence that either there is no intermediate phase between the quantum striped
phase and the FM phase for the case $J_{1}=-1$, or, if one exists, it can occur
only over a very narrow regime indeed.  This situation may be contrasted
with that of the AFM version of the model ($J_{1}=+1$),\cite{DJJF:2011_honeycomb}
where the LSUB$m$ results for the
gs energy using the striped model state terminate before they meet the
corresponding results using the N\'eel state as model state (which themselves
also terminated at some upper termination points that were lower in value than the
lower termination points for the striped state).  In the latter case there is
an intermediate plaquette valence-bond crystal (PVBC) phase.

At the classical level
the difference in the values of the gs energy per spin of the collinear striped states
between the two $s=\frac{1}{2}$ cases (i.e., for positive and negative values of $J_{1}$ with
$|J_{1}|=1$) is 0.25, independent of $J_{2}$ and $J_{3}$.  The quantum versions
follow this pattern for larger values of $J_{3}=J_{2}$, as seen from  Fig.~\ref{E},
but the constancy in the difference breaks down at around $J_{2} \approx 0.6$, where the AFM case
($J_{1}=+1$) exhibits a critical point marking a transition to the PVBC phase, which then in turn
undergoes a further phase transition to the N\'eel phase at another lower critical value.  The
corresponding best available CCM estimates for those two critical values for the AFM
case of the model with $J_1=+1$ are $J^{c_{2}}_{2} \approx 0.60$ and $J^{c_{1}}_{2} \approx 0.47$
respectively.\cite{DJJF:2011_honeycomb}   In the present FM case of the model with
$J_1=-1$ we see no evidence (apart from the seeming termination of the solutions
to the equations for the LSUB$12$ approximation based on the striped state as
CCM model state very slightly before the gs energy crossing point with the FM state) of any
similar intermediate state between the FM state and the collinear striped AFM state.  If any
such intermediate state exists at all, however, it must be confined to a very narrow region indeed
around $J_{2} \approx 0.11$, probably confined to $0.10 \lesssim J_{2} \lesssim 0.12$.  We
return to a more detailed discussion of this region later.  For the moment we note only that
it is much reduced from the region $0.1<J_{2}<0.2$ in which the corresponding classical
version of the model has the spiral phase V as its stable gs phase.

For the present FM case with $J_{1}=-1$ the CCM LSUB$m$ gs energy curves using the striped model
state cross the corresponding gs energy curve for the FM state from Eq. (\ref{H_classical}) for
$m=\{6,8,10\}$ at corresponding critical values $J^{c}_{2}(\rm{LSUB}6) \approx 0.1106$
(where $E^{c}_{\rm{LSUB}6}/N \approx -0.2506$), $J^{c}_{2}(\rm{LSUB}8) \approx 0.1101$
(where $E^{c}_{\rm{LSUB}8}/N \approx -0.2511$), and $J^{c}_{2}(\rm{LSUB}10) \approx 0.1098$
(where $E^{c}_{\rm{LSUB}10}/N \approx -0.2515$).  The corresponding LSUB$12$ result for the gs energy
using the striped state as the CCM model state appears to terminate just before meeting the
gs energy curve for the FM phase.  However we note that for such very high-order CCM
calculations it becomes very computationally expensive to determine the termination point with
high accuracy.  If we use the extrapolated LSUB$\infty$ results for the gs energy for the striped
phase by making use of Eq. (\ref{E_extrapo}) and employing the whole data set $m=\{6,8,10,12\}$,
we thus need to perform a further very small extrapolation of the CCM results to lower values
of $J_{2}$ to find the presumed crossing point of the energies of the striped and FM phases, in
the scenario in which these two phases meet at a first-order transition with no intermediate
phase (that would itself be confined to the very narrow intervening region
$0.10 \lesssim J_{2} \lesssim 0.12$, as discussed above).
As expected, simple power-law expansions give very accurate fits, and give crossing points
very close to those above.  Putting all the energy data together, our best estimate for the
critical point of the first-order phase transition from the collinear striped phase to the
FM phase (in the scenario where this transition occurs directly, with no intermediate phase
confined to the narrow region $0.10 \lesssim J_{2} \lesssim 0.12$)
for the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg
ferromagnet (with $J_{1}=-1$) on the honeycomb lattice, and with $J_{3}=J_{2}>0$, is
$J^{c}_{2}=0.1095 \pm 0.0005$, at which point the gs energy per spin is
$E^{c}/N=-0.2518 \pm 0.0006$.

We see from Fig.~\ref{E}(a) that
the agreement between the ED ($N=32$) and the CCM energies is very satisfactory.
Moreover, due to the finite-size scaling of the gs energy, $E/N = e_0-a/N^{3/2}$
with $a >0$ (and see, e.g. Refs.~[\onlinecite{schulz}] and [\onlinecite{ED40}]),
the difference between the CCM and the ED gs energies would become even smaller
if finite lattices of larger size could be considered. The ED turnover point in
the energy curve that marks the termination of the FM phase occurs at a value of about
0.1003 for the $N=32$ lattice used, and for the same reasons as above
this value will increase as $N$ is increased.  Thus, in summary, while the
CCM estimates for the gs energy per spin for the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
Heisenberg model on the extended infinite honeycomb lattice
are much more accurate than the ED results, the latter do serve as an
independent check on the former.

The hypothetical phase transition (i.e., when the existence of the intervening spiral phase V
is momentarily ignored) from FM order to collinear striped AFM order for the classical
version of the FM model with $J_{1}=-1$ occurs at a value
$J^{\rm cl}_{2}=\frac{1}{7} \approx 0.143$, compared with the corresponding
value $J^{c}_{2} \approx 0.110$ found here.  Thus quantum fluctuations act to
stabilize the collinear AFM order, at the expense of the FM order, to higher values
of frustration than in the classical case.  It is interesting to note that
a similar situation was found in the FM version
($J_{1}=-1, J_{2}>0$) of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$
model on the square lattice,\cite{Richter:2010} where a quantum critical point exists
at a value $J^{c}_{2} \approx 0.39$  for a similar transition from FM order to
collinear striped order, compared with a corresponding classical value of
$J^{\rm cl}_{2}=0.5$.  It is well known, from many cases studied, that quantum
fluctuations almost always favor collinear states over noncollinear ones (e.g.,
spiral or canted states).  What is interesting in both the present case and the
spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$ model on the square lattice cited above, is that
quantum fluctuations seem also to favor one collinear state (namely the collinear striped
AFM state in these two cases) where the quantum fluctuations are present,
over another collinear state (namely the FM state in these two cases) where quantum
fluctuations are absent.  It is intriguing to wonder whether these are examples of
a more general rule.

We present results in Fig.~\ref{M} for the CCM collinear stripe order parameter $M$, as
defined in Sec.~\ref{CCM}.  Figure~\ref{M}(a) shows LSUB$m$ results with $m=\{6,8,10,12\}$,
while Fig.~\ref{M}(b) shows the corresponding extrapolated CCM LSUB$\infty$ ($m \rightarrow
\infty$) results using both Eqs. (\ref{M_extrapo_standard}) and (\ref{M_extrapo_frustrated}).
\begin{figure*}[!t,b]
\begin{center}
\mbox{
  \subfloat[$m=\{6,8,10,12\}$]{\scalebox{0.3}{\includegraphics[angle=270]{fig3a.eps}}}
\hfil
\subfloat[$m \rightarrow \infty$]{\scalebox{0.3}{\includegraphics[angle=270]{fig3b.eps}}}
 }
 \caption{(Color online) Ground-state magnetic order parameter, $M$,
   for the striped AFM state of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
   honeycomb model with $J_{1}=-1$, compared with those for $J_{1}=+1$ (with $J_{3}=J_{2}>0$
   for both cases). The CCM results for
   various LSUB$m$ approximations with $m=\{6,8,10,12\}$ are shown in
   (a).  We also show in (b) the extrapolated LSUB$\infty$ results
   using the $m=\{6,8,10,12\}$ data points.  The curves labelled LSUB$\infty (1)$ and LSUB$\infty (2)$
   are obtained using Eq. (\ref{M_extrapo_standard}) and Eq. (\ref{M_extrapo_frustrated})
   respectively.  In all cases curves without symbols attached refer to the case $J_{1}=-1$,
   whereas the corresponding curves with symbols refer to the case $J_{1}=+1$.}
\label{M}
\end{center}
\end{figure*}
We note firstly that the CCM LSUB$m$ order parameter results depend on the
approximation level $m$ much more strongly than those for the gs energy.
It is clear that the order parameter behaves similarly for large values of
$J_2$ for both the FM model ($J_{1}<0$) and the AFM model ($J_{1}>0$).
However, once again there are considerable differences in the behavior of $M$
between the two models for values of the frustration parameter $J_{2}/|J_{1}| \lesssim 0.6$.
The extrapolated CCM results for $M$ for the AFM model in Fig.~\ref{M}(b) clearly show the
breakdown of the quasiclassical collinear magnetic LRO near the
critical value of $J_{2} \approx 0.6$, i.e., significantly above the classical
transition point $J^{\rm {cl}}_{2}=0.5$ (and see, e.g.,
Refs.~[\onlinecite{honey2,DJJF:2011_honeycomb,lauchli2011,honey7}]).
Indeed, the CCM estimate for the critical value of the frustration parameter
in the AFM case for the disappearance of collinear striped order is
$J^{c_{2}}_{2} \approx 0.60$ from the point at which $M$ becomes zero, using the extrapolation
scheme of Eq.~(\ref{M_extrapo_frustrated}).\cite{DJJF:2011_honeycomb}
By contrast, the order parameter for the FM model stays almost constant over the whole
parameter region shown in Fig.~\ref{M}.  We do not
observe any indication of the breakdown of the collinear striped
magnetic LRO until $J_{2} \approx 0.11$ for the FM model,
which is below the hypothetical classical transition point $J^{c}_{2} \approx 0.143$, as we
observed previously in the results for the gs energy.

Lastly, we present  results for various spin-spin correlation
functions for the FM as well as for the AFM model in Fig. \ref{CorrFunctn}.
Figure \ref{CorrFunctn}(a) shows the CCM LSUB10 results and
Fig.~\ref{CorrFunctn}(b) shows the corresponding ED results.
\begin{figure*}[!tb]
\begin{center}
\mbox{
  \subfloat[CCM LSUB10]{\scalebox{0.3}{\includegraphics[angle=270]{fig4a.eps}}}
\hfil
\subfloat[ED ($N=32$)]{\scalebox{0.3}{\includegraphics[angle=270]{fig4b.eps}}}
 }
 \caption{
  (Color online) Selected spin-spin correlation functions
  $\langle{\bf s}(0)\cdot{\bf s}({\bf r})\rangle$ for the spin-$\frac{1}{2}$
  $J_{1}$--$J_{2}$--$J_{3}$ model on the honeycomb lattice with $J_{3}=J_{2}$, for
  both the FM case (with $J_{1}=-1$) and the AFM case (with $J_{1}=+1$), using
  (a) the CCM with the striped collinear state as model state, at the LSUB$10$
  level of approximation; and (b) the ED method on a lattice of size $N=32$.
  Values $r=1, 1.732$ and $2$
  correspond respectively to NN, NNN, and NNNN pairs of spins.
  In all cases curves without symbols attached refer to the case $J_{1}=-1$,
  whereas the corresponding curves with symbols refer to the case $J_{1}=+1$.}
\label{CorrFunctn}
\end{center}
\end{figure*}
Once again we note that for large values of the frustration parameter $J_2$
the corresponding spin-spin correlations functions for both the FM ($J_{1}=-1$)
and AFM ($J_{1}=+1$) models agree remarkably well with one another for
both the CCM and ED calculations.  Furthermore, for the FM model the agreement
of the CCM correlation functions with the ED data is excellent.  For the AFM model
the agreement between the CCM and ED results is again excellent for values of $J_2$ above
the transition point at which the AFM collinear striped order disappears, namely
$J^{c_{2}}_2 \approx 0.60$, but around and below this value there are noticeable
differences.  In particular, the very steep
change in the correlation functions at $J_{2} \approx 0.62$ present in
the ED ($N=32$) data for the AFM model is not observed
in the CCM LSUB10 data. Instead the CCM data show a smoother change in that region.
However, we have argued\cite{DJJF:2011_honeycomb} that for $J < J^{c_{2}}_{2} \approx 0.60$
no striped magnetic LRO order exists.  Indeed we argued that no magnetic LRO order
exists at all for the AFM model in the regime $J^{c_{1}}_{2} < J < J^{c_{2}}_{2}$, where instead
we have a PVBC state.  Hence, it is not
surprising that the CCM solution in a finite order of LSUB$m$
approximation based on the collinear stripe reference state
does not provide such accurate results for the correlation
functions inside this magnetically disordered phase.

To conclude, we return to examine more closely the very narrow region
$0.10 \lesssim J_{2} \lesssim 0.12$ for which our CCM results based on the
striped AFM state as model state could not exclude the possibility of an intervening
phase between the striped AFM and the FM phases.  In Fig.~\ref{CorrFunctn_zoom}
\begin{figure}[!tb]
\begin{center}
\includegraphics[width=6cm,angle=270]{fig5.eps}
\caption{(Color online) An expanded view near the FM boundary of the same spin-spin correlation functions
$\langle{\bf s}(0)\cdot{\bf s}({\bf r})\rangle$ shown in Fig.~\ref{CorrFunctn}(b)
for the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ model on the honeycomb lattice for
the FM case with $J_{1}=-1$ and $J_{3}=J_{2}$ using the ED method on a lattice of size $N=32$.}
\label{CorrFunctn_zoom}
\end{center}
\end{figure}
we show a more detailed view of the ED results for the same spin-spin correlation
functions shown in Fig.~\ref{CorrFunctn}(b) in this narrow region
just above the FM transition point.  The ED data does definitely indicate the
existence of a phase in precisely the region $0.10 \lesssim J_{2} \lesssim 0.12$.
It is difficult from this data to say with any certainty whether or not the state
is the quantum-mechanical remnant of the classical spiral phase V that exists in the classical
regime $0.1<J_{2}<0.2$.  Furthermore, without ED calculations on larger lattices, for which the
computational cost would be prohibitive, it is also not possible to say whether these results
over such a narrow region are an artefact of the finite lattice size.  Our results are summarized in
Sec.~\ref{conclusions}.

\section{Summary and Conclusions}
\label{conclusions}
In this paper we have presented results on the gs properties of the
spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ Heisenberg model with FM
NN ($J_{1}=-1$) exchange bonds in the presence of frustrating AFM NNN ($J_{2}>0$)
and NNNN ($J_{3}>0$) exchange bonds of equal strength ($J_{3}=J_{2}$)
on the honeycomb lattice, using both the CCM and Lanczos ED.
By comparison with previous studies for the AFM ($J_{1}=+1$)
version of the model,\cite{DJJF:2011_honeycomb} we find similar behavior for
both models for values $J_{2}\gtrsim 0.6|J_{1}|$, but for values of
$J_{2} \lesssim 0.6|J_{1}|$ the models differ markedly.  The results of the present
paper for the FM version of the model and that of the previous paper \cite{DJJF:2011_honeycomb}
for the AFM version may conveniently be combined and summarised in the phase diagram
shown in Fig.~\ref{phase-diagram}.
\begin{figure}[!tb]
\begin{center}
\includegraphics[width=11cm]{fig6.ps}
\caption{(Color online) The phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$ honeycomb model
in the $J_1$-$J_2$ plane, for the case $J_{3}=J_{2}$.  The continuous transition between the AFM N\'eel  and PVBC phases at
$J_{2}/J_{1} \approx 0.47$ is shown by a broken line, while the first-order transition between the PVBC and AFM striped phases
at $J_{2}/J_{1} \approx 0.60$ is shown by a solid line.  Our results indicate that the transition
between the striped AFM and FM phases is either a first-order one at $J_{2}/J_{1} \approx -0.11$ or occurs via an intermediate
phase, probably with noncollinear spiral order, which exists in the region $-0.12 \lesssim J_{2}/J_{1} \lesssim 0.10$.
The region between the FM and AFM N\'eel phases with $J_{3}=J_{2}<0$ has not been investigated by us.}
\label{phase-diagram}
\end{center}
\end{figure}

We note that, by contrast with the corresponding model with AFM NN exchange ($J_{1}=+1$)
we do not find indications for a non-classical magnetically-disordered phase
for the model with FM NN exchange ($J_{1}=-1$).  If such a phase exists at all
it must be confined to a very small range of
the frustration parameter around $0.10 \lesssim J_{2} \lesssim 0.12$.
However, any such phase is much more likely to be a quasiclassical remnant of the
spiral phase V that exists in the corresponding classical model (with $J_{1}=-1$)
in the parameter regime $0.1<J_{2}<0.2$.  As expected, quantum fluctuations then usually favor
a collinear phase over a noncollinear one, and the extent of any spiral phase is
smaller in the quantum spin-$\frac{1}{2}$ case than in the classical ($s \rightarrow 0$)
case.

In one scenario the results presented here for the case $J_{1}=-1$ indicate a direct
first-order transition between the two magnetically ordered
phases, namely  the FM ground state at small values of the frustration parameter $J_2$
and  the striped collinear AFM ground state at larger values of $J_2$.
Our best estimate of the phase transition point is then $J^{c}_{2}=0.1095 \pm 0.0005$.
Although in this scenario a quasiclassical gs phase
(viz., the collinear striped AFM state) exists in the
whole parameter space down to the FM gs phase, the
frustration might still have a strong effect on
the low-temperature thermodynamics near the transition
point at $J^{c}_{2}=0.1095 \pm 0.0005$.\cite{haertel10,Richter:2010}
For values $J_{2} \gtrsim J^{c}_{2}$ the FM multiplet becomes a low-lying
excitation, and this might lead to an additional low-temperature peak
in the specific heat $C(T)$.\cite{shannon04,HMeisner:2006,HTLu:2006}
We note that indications for such  an additional low-temperature peak
in $C(T)$ were also found on the FM side near such a
transition\cite{haertel08,haertel10} (i.e., at $J_{2}
\lesssim J^{c}_{2}$) in other frustrated spin models.

In an alternative scenario our results also indicate the possibility
of an intervening phase between the collinear FM and striped AFM phases.  Any such phase,
however, is limited to lie within the very narrow range $0.10 \lesssim J_{2} \lesssim 0.12$,
as shown in Fig.~\ref{phase-diagram}.  In principle we could more accurately establish
the existence of such a phase as a quasiclassical remnant of the classical spiral phase V,
and thence also more accurately establish its phase boundaries, by performing another
comparable set of CCM calculations to those performed here with the striped AFM state as
model state, but using instead the spiral state V as model state.  Such calculations
would be much more onerous and computationally expensive, however, since on the one hand the number
$N_f$ of fundamental CCM configurations at a given LSUB$m$ level is greater for the spiral
model state than for the striped model state and, furthermore, the CCM results would need to be
optimized at a given LSUB$m$ level with respect to the spiral pitch angle parameters by minimizing
the corresponding result for the energy per spin separately for each set of values
for the bond strength parameters.

We note finally that we have not yet investigated the present model in the case where
$J_{3}=J_{2}<0$.  For the FM version of the model when $J_{1}<0$ also, the FM phase
is then obviously the stable ground state.  Conversely, when $J_{1}>0$ and frustration occurs,
there is a direct first-order transition in the classical version of the model between
the FM and N\'eel AFM states at a value $J_{2}/J_{1}=-1$.  Following the discussion in
Sec.~\ref{results} we might expect that quantum fluctuations could again act either (a) to retain
the direct transition but to stabilize the collinear AFM order in preference to the FM order,
thus pushing the phase boundary to a somewhat lower value, $J_{2}/J_{1}<-1$, for the spin-$\frac{1}{2}$
case; or (b) to permit an intervening state with no classical counterpart.
Indeed, very preliminary CCM calculations indicate that scenario (a) is realized and
that this corresponding critical point may be pushed to a value $J_{2}/J_{1} \approx -1.15 \pm 0.05$.
We hope to report in more detail on this region and to give
a more accurate value of this phase boundary in a future paper.

As discussed briefly in Sec.~\ref{intro}, it has been proposed
\cite{shannon06,shannon09,sindz09,momoi2011} that the competition between FM Heisenberg
interactions between NN pairs of spins and AFM interactions between other spins in
frustrated spin-$\frac{1}{2}$ systems on the square lattice could lead to gapless
spin-liquid states with multipolar order (e.g., spin-nematic states) adjacent
to the FM state.  Similar states have also been proposed to arise in frustrated multiple
cyclic spin-exchange models on the triangular lattice with FM NN
pairwise interactions, \cite{momoi2006} either in the presence of a magnetic field
(where octupolar order occurs) or in its absence (where quadratic or nematic ordering
occurs in a state bordering the FM state).  In the case of the frustrated honeycomb-lattice
ferromagnet considered here we have found no evidence for such states.  However,
the multipolar-ordering phenomenon in the zero-field case considered here is
evidently rather fragile, and in the square-lattice case
for the spin-$\frac{1}{2}$ FM version of the $J_1$--$J_2$ model
(i.e., with $J_{1}<0$) even their existence has
been questioned in recent rather accurate work \cite{Richter:2010} that also
employed both high-order CCM and ED techniques.  No evidence was found for such states
either in a very recent Schwinger boson study on the square lattice,\cite{Feldner:2011_J1J2J3mod}
using the same FM version of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{3}$
Heisenberg model that we studied here on ther honeycomb lattice.
Nevertheless, the history of the study of quantum magnets has shown us
that the detection of phases
with novel quantum ordering, such as nematic states of various kinds, is
extremely subtle.  In particular, the present honeycomb-lattice model surely
warrants further investigation before the absence of nematic states in the
FM case discussed here is considered definite.

Finally we mention that frustrated ferromagnets are also interesting
with respect to
multi-magnon bound states appearing in high magnetic fields (and see, e.g.,
Refs.~[\onlinecite{shannon06,Kecke07,Sudan09,nishimoto2011}]).  The
present model also warrants further investigation when the coupling
to an external magnetic field is included.

\section*{ACKNOWLEDGMENTS}
We thank the University of Minnesota Supercomputing Institute for
Digital Simulation and Advanced Computation for the grant of
supercomputing facilities, on which we relied for the
numerical calculations reported here. One of the authors (DJJF) acknowledges and
thanks the European Science Foundation for financial support under the
research network program ``Highly Frustrated Magnetism'' (short visit grant number 3858).

redpajama_set_name: RedPajamaArXiv


text:
Julia Banks: Exiting Australia MP decries 'bullying' of women
By BBC
MP Julia Banks (L) was a supporter of former Prime Minister Malcolm Turnbull
(BBC) – An Australian government MP has revealed she will not contest the next election, condemning the parliament's "bullying and intimidation" of women.
Julia Banks branded a party coup that ousted Malcolm Turnbull as PM last week as "the final straw" in her decision.
In a withering statement, Ms Banks took aim at the "scourge of cultural and gender bias" in politics and society.
In recent years, Australian female MPs have accused male counterparts of "misogyny" and "slut-shaming".
Amid wide-ranging and chaotic infighting last week, the government faced an allegation that male party figures had "stood over" female MPs in a bid to secure enough signatures to topple Mr Turnbull. Others denied the assertion.
Earlier this year, the government launched a national inquiry into workplace sexual harassment.
Who did Ms Banks criticise?
The Liberal Party MP, who holds a marginal seat in Melbourne, did not make reference to specific incidents.
However, she said in a statement: "I will always call out bad behaviour and will not tolerate any form of bullying or intimidation. I have experienced this both from within my own party and the Labor party."
"In anticipating my critics saying I'm 'playing the gender card' – I say this. Women have suffered in silence for too long and in this last twelve months the world has seen many courageous women speak out," she added.
A supporter of Mr Turnbull and Julie Bishop – who was replaced as party deputy last week – Ms Banks also made a more general criticism about the political turmoil, rebuking unnamed figures with "mean-spirited grudges intent on settling their personal scores".
She said she would support new Prime Minister Scott Morrison and party deputy Josh Frydenberg.
How have others responded?
Mr Morrison said he had "no truck with bullying or intimidation in whatever form it is".
"I have laid down the law to my ministry and to the parliamentary secretary ranks of my government," he said on Wednesday.
Minister for Women Kelly O'Dwyer, who called herself a friend of Ms Banks, said workplace bullying "whether on the shopfloor, or in our nation's Parliament, [was] totally unacceptable".
"I deeply regret the decision that Julia has made today… and the circumstances that have led to her decision to leave politics".
What has been controversial previously?
Under Tony Abbott's leadership in 2013, the centre-right government was criticised for having just one woman in a 19-member cabinet – although it has since added more.
Allegations of gender-based bullying have also hit Labor: one MP, Emma Husar, asserted on Wednesday that her career had been ruined by malicious "slut-shaming".
In recent times, Australian politics has also heard:
Julia Gillard, as prime minister in 2012, accuse Mr Abbott of "misogyny" in a parliamentary speech that went viral;
Sarah Hanson-Young, a senator, say she had been "slut-shamed" by a male political opponent;
Reports that Ms O'Dwyer was asked to consider expressing milk to avoid missing parliamentary duties in 2015, prompting a backlash.
More International News Stories
East Africa: Worst locust swarms in 25 years could worsen food crisis January 17, 2020
Pregnant woman and six children tortured and killed by a religious cult in Panama, authorities say January 17, 2020
Thai woman bitten by snake while sitting on toilet January 17, 2020
Deaf man from Brooklyn sues Pornhub over lack of closed captioning January 17, 2020
Missing Polish farmer believed to have been eaten by his own pigs January 17, 2020
US woman charged with leaving 6 kids with dead man January 17, 2020
Ukrainian prime minister submits resignation after tapes January 17, 2020
Woman gets 25 years in jail for fatally poisoning husband with eye drops January 17, 2020
JetBlue Airways is raising checked-bag fees again January 16, 2020

redpajama_set_name: RedPajamaCommonCrawl


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Station Barcelona La Sagrera - TAV, kort Sagrera | TAV (Catalaans: Estació de Sagrera - TAV, Spaans: Estación de Barcelona - La Sagrera - TAV is een groot toekomstig spoorwegstation in het noordoostelijk deel van het stadscentrum van Barcelona parallel liggend aan en zo'n 600 meter oostelijker liggend van de Avinguda Meridiana.

De bouwwerken begonnen in 2009, maar werden van 2015 tot 2018 lamgelegd. In 2022 wordt verwacht dat het in 2023 volledig wordt geopend. Naast het station zelf werd ook een 5,78 km lange spoortunnel gebouwd, geschikt voor hogesnelheidsverkeer die het nieuwe station verbindt met Barcelona Sants.

Het station wordt een spoorwegknooppunt in de stad Barcelona, gelegen in de wijk La Sagrera van het district Sant Andreu, evenwel net tegen de grens met het district Sant Martí. Het is ingepland op de locatie waar tot de jaren negentig een belangrijk goederenstation van de stad gelegen was, station dat begin 21e eeuw verlaten werd, en in 2007 werd afgebroken.

Het station wordt een intermodaal treinstation waar hogesnelheidstreinen, lange- en middellangeafstandsdiensten en forensentreinen stoppen, en overgestapt kan worden in een onderliggend gelijknamig metrostation op de metrolijnen L4, L9 en L10.  Tevens is een intercitybusstation in het knooppunt gevestigd. Om de verschillende treindiensten toe te laten zullen acht sporen afgewerkt worden in normaalspoorbreedte, voor AVE, Avant, TGV, Alvia en Euromed lijnen, en zullen acht sporen in Iberisch breedspoor opgeleverd worden voor de andere lange- en middellangeafstandsdiensten zoals de lijn R11 van de Rodalies de Catalunya en de forensentreinen van de Rodalies Barcelona, meer bepaald de lijnen R1 en R2.

Bij voltooiing wordt het station het grootste gebouw in de stad, en de grootste spoorweginfrastructuur in Catalonië. Het gebouw is ontworpen om tot honderd miljoen passagiers op jaarbasis te behandelen, en heeft afmetingen vergelijkbaar met de in 2009 in gebruik genomen Terminal 1 van de Aeroport Josep Tarradellas Barcelona-el Prat luchthaven.

Zie ook
 Lijst van spoorwegstations in Barcelona
 Lijst van spoorwegstations van Rodalies Barcelona

Barcelona S
Barcelona La Sagrera - TAV
Bouwwerk in Barcelona

redpajama_set_name: RedPajamaWikipedia


The event begins at 9.00am and is free and open to the public; in the case of inclement weather, the event will be held on Sunday, May 1.
Clearwater Middle School competes in the obstacle course at the 2015 ROV Challenge hosted by BIOS.
A spokesperson said, "Globally, HSBC focuses on supporting educational initiatives which promote learning about the environment. In Bermuda, HSBC has partnered with BIOS for the past 2 years in support of the MARINE Programme and the ROV Challenge, which teaches young people about the world's oceans, and the importance of preserving them.
"It also supports education goals associated with science, technology, engineering, and mathematics, known as the STEM fields.
"For the 2016 piloting challenge, MARINE will be partnering with the Marine Advanced Technology Education [MATE] center to host a regional challenge. Students will be competing at two levels, as designated by MATE.
"Beginners will compete at the Scout level and more advanced students at the Navigator level. Students will complete the event on the same challenge course as other MATE regional partners internationally.


I warmly welcome the new use of Mount Carmel Hospital as a dedicated community hospital for Dublin, with an allocation of 65 beds, as part of the HSE Service Plan for 2015, which was published today.
The Minister for Communications, Energy and Natural Resources, Alex White, T.D., today published online national and county maps that identify the homes, businesses and schools where commercial providers will deliver high-speed broadband access by the end of 2016. Minister White said that the State would invest in all the remaining areas to ensure that every home, school and business in Ireland has access to high-speed broadband, regardless of where it is located.
Here's a short video of my speech yesterday in the Dáil on the water package reforms announced on Wednesday by Minister Kelly. These reforms bring simplicity, certainty and affordability to every family and individual in Ireland and represent a fair and reasonable approach to addressing our poor and deteriorating water and sewerage infrastructure.
It is a pleasure to be here tonight at the eighth annual Dún Laoghaire EnviroCom Awards. I will try to keep my speech brief as I know you're all looking forward to your meal.
The purpose of tonight's EnviroCom Awards is to recognise businesses and agencies in Dún Laoghaire Rathdown for their environmental achievements. The Awards celebrate excellence, innovation, dedication and success in environmental management in our community. The awards shine a light on the range of actions that businesses and agencies can take to minimise their impact on the environment and in many cases save money and lower costs.
I was very saddened to hear of the death of Brian Farrell, who was among the very best of Irish broadcasters. He had an exceptional insight into Irish politics and current affairs, and he will be remembered as a rigorous and fair analyst and interviewer. He will be very much missed and my thoughts today are with his family.
Local jobseekers who avail of temporary seasonal work for up to 8 weeks over Christmas should know that their social welfare payment will be immediately reinstated when the period of employment ends.
It is around this time of year that temporary seasonal work opens up as the Christmas retail rush gets underway. I want to assure people on either Jobseeker's Benefit or Jobseeker's Allowance that, should they take up employment over the holidays, this payment will immediately resume once that employment ends.
I warmly welcome the latest CSO figures which show that in the past year there has been a 5.2% drop in the numbers signing on the live register at Nutgrove Social Welfare Office and an 11.6% drop at the Intreo Centre in Dún Laoghaire. These are really positive developments and signal strong progress in renewing our local economy.


LONDON, ON., Dec. 6, 2016 –Today the McCormick® Flavour Forecast® 2017 – the go-to guide for trends and ingredients set to excite taste buds around the world – was released by McCormick & Company, Incorporated, a global leader in flavour.
For nearly two decades, this much-anticipated annual report from McCormick has predicted emerging flavours – like chipotle chilies, coconut water and Harissa sauce – that are now found everywhere from restaurants to retail shelves and kitchen cabinets.
Rise & Shine to Global Tastes – Breakfast options with big, global flavours are being sought after by a generation of flavour adventurists not content with the same boring bowl. Try warm, sweet congee or a Middle Eastern-inspired breakfast hash topped with a spicy skhug sauce.
Taste It: Breakfast Hash with Skhug Sauce (Link online) - Tender chickpeas, ground lamb or beef and roasted vegetables seasoned with a blend of coriander, cumin and fennel.
Say It: Skhug [shug], this complex Middle Eastern hot sauce is made with Thai bird eye chilies, cumin, cardamom, coriander, garlic, parsley, cilantro, olive oil and lemon juice.
Plancha: Flat-Out Grilling – Hailing from Spain, France's Basque region as well as Mexico, the plancha (a thick, flat slab of cast iron) is growing in popularity around the world for creating a sizzling, smoky sear and flavour crust. Grillers can easily use the plancha with meats, seafood and vegetables, paired with bold sauces, rubs and glazes.
Taste It: Espelette Pepper-Rubbed Steak a la Plancha (Link online) - a zesty, Mediterranean-herb rub enhances juicy steak grilled on a sizzlin' hot plancha.
Say It: Espelette [es-PE-let] pepper, originating from the Basque region of France, delivers a distinctively smoky, sweet and mildly hot flavour.
Egg Yolks: The Sunny Side of Flavour – Egg yolks leave breakfast behind! Whether poached, fried or cured, chefs are pairing these indulgent golden gems with a range of spices, herbs and sauces on lunch and dinner menus.
Taste It: Mediterranean Vegetable Shakshuka (Link online) - Sunny-side-up egg yolks simmered in a tomato and vegetable sauce make a rustic supper.
Say It: Shakshuka [shahk-SHOO-kah], flavoured with a savoury spice blend of smoked paprika, cumin, pepper, cayenne, turmeric and caraway.
Modern Med – Discover the new cuisine for the 21st century - melding Eastern Mediterranean ingredients with Western European classics.
Taste It: Persian Minestrone (Link online) - Persian Ash-e reshteh meets Italian minestrone.
Say It: Ash-e Reshteh [OSH-e-resh-tay], a thick, hearty soup made with beans, herbs, turmeric and flat noodles.
Taste It: Dragon Fruit & Strawberry "Poke" with Pepper Syrup (Link online) - Fresh strawberry and diced dragon fruit salad atop a dollop of peppered whipped cream and crispy wontons.
Say It: Poke [po-kay], create this unique take on Hawaiian poke salad with a drizzle of balsamic-pepper syrup.
To view and explore the full Flavour Forecast 2017 report, visit www.Clubhouseforchefs.ca.
McCormick & Company, Incorporated is a global leader in flavour. With $4.3 billion in annual sales the company manufactures, markets and distributes spices, seasoning mixes, condiments and other flavourful products to the entire food industry – retail outlets, food manufacturers and foodservice businesses. Every day, no matter where or what you eat, you can enjoy food flavoured by McCormick. McCormick Brings Passion to Flavour™. For more information, visit www.mccormick.ca.


For just over 1 weekend, our team captured the installation of the new bridge over the M1 in Leicestershire. In the video, a huge trolley was put together on the carriageway which was then used to slide the constructed bridge across the motorway. This bridge will help alleviate traffic travelling through local villages and forms part of the Kegworth Bypass.


I just listened to Arianna Huffington speak about her project, Thrive Global, from No Limits with Rebecca Jarvis.
I was instantly hooked. And that's how I found this amazing new resource.
You see, I have tried to live my life for several years now, in ways Ariana speaks about. I turn off my phone at night, because I've noticed I sleep better. I recognize the importance of not letting technology control me, I have always had old outdated versions of smart phones … with limited access to apps. I have been laser focused on getting the important things done, like a project slapped on my desk in the afternoon that must be filed the next day.
I have also been good about saying no to the less important things so I can make room for what's more important to me and what I want out of my life.
I have always guarded my creative capacity, because I am a creator. If I could be paid for it, I would love the opportunity to tinker away in a lab and experiment and create.
It seemed to be working. But then my boss moved, and I got laid off. It's only been a few months, and I think I need to be patient.
But, I am at a juncture in my life where it feels like my desire to guard my creative capacity and make it in the "real world" might not be working. I work in IP law. I have an electrical engineering background, I have five years under my belt as a patent attorney. Supposedly, I have some valuable skills.
I'm at place where for some reason it seems like the old school method is winning, and my method is losing. When I was employed, I noticed that everyone around me was stressed, working 9 to 10 hour days, even on the weekends. Despite some fears that I was falling behind, I kept saying "no" to distractions, and "yes" to what was important. Now I find myself wondering if I've fallen so far behind that I won't be able to catch up.
I hope to figure out how to make it work so I am gainfully employed again and I continue to get eight hours of sleep at night and thrive.
But I find myself wondering if maybe we all have to go through the wringer first before we can slow down and thrive? Maybe we have to make it to the level of Jeff Bezos before we are afforded the luxury of eight hours of sleep at night? Maybe we have to burn out first and ride on the momentum we created on our way to the top before we can slow down? Or is there another way to march to a "slower" beat, and maximize our potential throughout our life?
I haven't figured it out yet, but I hope to one day.
I am a second generation immigrant and also the daughter of genocide survivors. Electrical Engineer by trade, turned Patent Attorney.


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What's happening, everybody? Welcome to Chels Meets World. For those of you who are new here, I'm Chelsea, the blogger of this shindig. For those of you just coming back through, thanks for coming!
I am humbled to bring you all my first article in the Individuals category of my blog. I created this category because one of my top value strengths is something called Appreciation of beauty and excellence (S/O to URI Leadership 😊).
In short, this means I value individuality. I love getting to meet people and learn about what makes them who they are. As a journalism major, I am also passionate about telling one's story. So, I guess you can say this is going to be one of my favorite sections of the blog.
So, without further a due, allow me to introduce you to,
Erica Herron.
A Jersey girl, with a little Florida Sunshine:
Erica Herron is a photographer. Did Herron always know that she wanted to be a photographer? Not at all. Coincidentally, she stumbled upon the profession while looking for jobs.
Herron born and raised in South Jersey moved to the sunshine state of Florida at the age of 16. It
Erica Herron | Red Jacket Photography By E
was a few years later when a friend of hers who had just finished Basic Training with the U.S. Air Force came back to Florida to visit. But he did not just come back by himself, he came back with a friend. A friend who eventually would become Herron's best friend and now husband.
"Before I met my husband," said Herron. "I used to say to myself that I would never want to marry someone in the military. But I wouldn't change it for anything."
After Herron got married and she and her husband were set to move to Georgia. Before the move, she started looking for jobs and came upon an opening at a studio called Picture Me Portrait Studios. It was here where she would learn the ropes. She would also discover her love to "see [the] beauty [in photography] in ways that not your average every-day person would normally see."
While working there Herron would be challenged to "think outside the box." The camera in the studio was mounted on a counter and the photographers needed to be able to sell their photos to customers in order to get paid. This motivated Herron to give the customers the best of the best.
"I would draw little stick figures of how I could pose people," Herron explained. "I would look up How to pose people on Pinterest or YouTube. I did a lot of research because I wanted to go far and beyond for people."
Work Hard Play Hard:
After learning the ropes from the studio, she started venturing into her own camera. Herron did admit that in the beginning, it was "more money-driven."
"I feel like a lot of photographers just starting out have made the mistake of being so concerned with making money," Herron said. "Eventually I started doing events rather than portraits."
As a civilian, Herron had the opportunity to work with different organizations on the base. In these roles, she was also able to make connections.
"People get to know you," she explained. "You're not just another face in the crowd. Once people know you're a photographer that's pretty much it because you'll get referred to by one person and then another."
Herron would go on to work on events such as an Air Force ball and Christmas parties for the squadrons on base. She was grateful to have a small team of friends who were willing to help her out.
It's the little things:
Once Herron and her husband moved to their next base (Aviano Air Base, Italy), Herron decided to retire her camera for the first few years. She admitted, she didn't really care to pick up her camera. Mainly because she was more focused on building her career in finance. But after having her daughter she decided to pick up her camera again.
"It kind of just kept going from there because my mind and my eyes had taken this break," said Herron. "I started to see things differently. I no longer saw my photography as a money-maker anymore."
Herron realized she really enjoyed capturing the beauty in small things of the world. She talked about how beautiful an abandoned building can be. How once she sees it she can practically picture the entire shoot in her mind.
"Some photographers that focus on landscape photography might just see it as a landscape shot," she explained. "But for me, I swear I can see the beauty of the model and the beauty of the abandoned building and how the two can come together."
One of Herron's favorite photos is Black and White. She admits that you can't turn every picture Black and White, but for the majority, you can.
"It creates an emotion in the picture," she explained. "Because it stripes the color out for a minute, and allows you to focus on what is actually there."
Recently she did a photo series in Black and White on her husband, while he was washing his car. She explained that she wanted to show how much work he was putting into washing his car.
"I didn't want to show what kind of car it was, I didn't want to show if it was gloomy out or sunny, I didn't want to show whether the car was green or yellow," she said. "I wanted people to see the action of the water, how he looks while washing the car, what a man looks like while washing a car."
"Because it's those little small things that are important. Even though most people were like, "oh my god not the Jordan's!" She added.
Getting Published:
One evening while Herron was going through her Facebook feed, a photographer she followed shared a post. The post was in search of photo submissions for Creative Collective Magazine created by a photographer to showcase other photographer's work. At the time Herron had just completed a laundry series with her friend Jennifer.
"Jen is an amazing model," Herron said. "She gets in front of the camera and turns into a whole different person, and I think it's beautiful to see."
Herron thanks Jennifer for all the sessions they've done together because it allowed her to broaden her love for creative photography.
Herron has been published about 20 different times in various magazines. One of her most humbling experiences was with Portraiture Magazine. A magazine that Herron says is "absolutely beautiful."
"It's run by Sarah [Lindsay]," she said. "She does phenomenal work from beginning to end. In this magazine, she put tips on how to continue your business even while quarantined."
Little things that Herron says can be very beneficial to photographers during these times. The theme for this publication was Happiness and Joy. To Herron's surprise, a photo she had submitted to be featured on the inside of the magazine was the one chosen for the cover.
"I remember getting the email, while I was sitting on the couch with my kids," Herron said. "And I instantly started to cry tears of joy. My aunt even face-timed me when it was published to say how beautiful it looks on the cover."
The photo was during a session she did with a couple. A couple who Herron says was one of her favorite sessions based on the couple's "pure true love." Herron admitted that she had previously submitted this photo to four other publications prior and none had chosen the photo. She was honored.
She explains how humbling and important it is to recognize another photographer's work. She knows as a photographer, she sometimes forgets that her work is worth looking at.
"Because we're just so used to seeing our photos all the time. So, when other people recognize your work, you start to think "wow is it really that good?"
The journey is just beginning:
As Herron and her family's time in Italy will be coming to a close, she is grateful for all she's learned. She is reminded that as a military spouse she is fortunate to have the benefit to travel to many places and build her network.
"To network with other photographers and to see how they view photography and learn from them," she said. "It's been nice because now I feel like I am more in my skin when it comes to photography versus before."
When asked what is one of Herron's most rewarding parts of being a photographer in her opinion, she said her son.
"I love when he comes up to me and asks Do you have a shoot today Mom? or Are you editing? Can I see? " she said. "He is just always there. I don't care if anyone else doesn't like my photos, but knowing that he does care means everything."
A special thank you to Erica for allowing me to feature her for the first post in the Individuals Series via Chels Meets World. If you or someone you know may be interested in checking out some of Herron's work please check out her page at www.Facebook.com/redjacketphotographybyE or via Instagram, @RedJacketPhotos. To see her cover photo on Portraiture Magazine, please follow this link.
Stay tuned for more within the Individuals Series, via Chels Meets World.


Our guide to Cleveland will help you find the best green spots in Cleveland Ohio. Cleveland has the resilient, no-nonsense attitude of any hard-working, Upper Midwest city. It's rock and roll, football and beer, and polka and kielbasa. And although it hasn't blinked as some of the elements of its 1990s renaissance have faded a bit, the long-term trend is still toward improvement. While some efforts have failed, new restaurants and nightspots have joined old favorites to give the city an impressive variety of entertainment options and a cultural diversity that might come as a surprise to first-time visitors. There are tons of great green spots in the city of Cleveland, our city guide will help you find the best green spots. You may have a hard time deciding what to do in Cleveland, but we make your decision easy.
10325 Cascade Xing, (216) 267-8360 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
12706 Larchmere Blvd, (216) 707-3333 - Vine and Bean Cafe is a green restaurant located in Cleveland OH.
135 Market St, (440) 835-4539 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
14881 Detroit Ave, (216) 221-9100 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
15029 Pearl Rd, (440) 846-9625 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
15601 Waterloo Rd, (216) 862-4895 - Cafe Marika is a green restaurant located in Cleveland OH.
17999 Bagley Rd, (440) 243-5041 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
21029 Ctr Rdg Rd, (440) 356-3109 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
24369 Cedar Rd, (216) 291-1686 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
2783 Euclid Hts Blvd, (216) 320-0280 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
33599 Aurora Rd, (440) 542-0017 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
3471 Steelyard Dr, (216) 661-6750 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
4015 Richmond Rd, (216) 378-1967 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
6901 Rockside Rd, (216) 986-0551 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
7707 W Ridgewood Dr, (440) 845-8400 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
9761 Vis Way, (216) 662-6402 - Chipotle Mexican Grill is a green restaurant located in Cleveland OH.
13212 Shaker Sq, (216) 751-7656 - North Union Farmers Market is a green farmers market located in Cleveland OH.
15000 Woodworth Rd, (216) 249-5455 - Farmers Market is a green farmers market located in Cleveland OH.
28560 Miles Rd, (440) 248-5222 - Miles Farmers Market is a green farmers market located in Cleveland OH.
8875 Rdg Rd, (440) 237-7888 - Romano's Farmers Market & Deli is a green farmers market located in Cleveland OH.
11798 Detroit Ave - Ecology Store Hempfields is a green store located in Cleveland OH.
26300 Cedar Rd, (216) 292-2276 - Teavana is a green coffeeshop / cafe located in Cleveland OH.
There are plenty more green spots in Cleveland.
See all green spots in Cleveland Ohio.


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NDA REVIEW RESOURCE MANAGEMENT/SCHEDULING SYSTEM IS UNDER CONSIDERATION BY FDA, COMMISSIONER KESSLER TELLS SEN. GLENN HEARING
The Pink Sheet pinkeditor@informa.com
FDA may develop a NDA resource management system to improve the planning and scheduling of NDA reviews and thus avoid unnecessary delays, Commissioner Kessler said at a July 25 hearing of the Senate Governmental Affairs Committee. Kessler and Center for Drug Evaluation & Research Director Carl Peck, MD, "are beginning to identify initiatives to improve the drug review process," the commissioner explained. "For example, I hope to develop a resource planning and scheduling system which will allow the [new drug review] division directors to define critical timeframes and to schedule resources to avoid bottlenecks," he said. Under the concept, the entire center would track its activities so that review timeframes are met. The commissioner was updating the committee on FDA's efforts to enhance its product review efficiency and to streamline and strengthen its enforcement actions. Chairman Glenn (D-Ohio) called the hearing to discuss the HHS (Edwards) Advisory Committee's report, which said FDA illustrates the "hollow" regulation by underfunded federal agencies. Kessler also announced that FDA has "set a goal of automating all NDA reviews by 1995." Noting that the agency is continuing its "very promising pilot test" of computer-assisted NDAs (CANDAs), the commissioner said analogous uses of automated marketing applications are being explored in the agency's other centers. Glenn closely questioned Kessler about how FDA's funding requests have fared in the Bush Administration. The Ohio Democrat noted that FDA's original request for fiscal 1992 funding was $ 987 mil. but was eventually scaled back to $ 770 mil., $ 196 mil. of which was proposed to come from user fees rather than appropriations. Repeating a phrase he used at Rep. Waxman's (D-Calif.) recent House Health Subcommittee hearing on FDA enforcement legislation ("The Pink Sheet" July 22, p. 7), Kessler replied that the Administration ought to "speak with one voice." The commissioner explained that "I need to deal with what I control." But he emphasized that the $ 770 mil. spending level in the President's budget request "is very important for us." When Glenn again emphasized the $ 987 mil. original request, Kessler suggested that the current focus should be on the $ 770 mil. goal. Congress is likely to appropriate an amount between the Senate proposal of $ 738.7 mil. and the House proposal of $ 761.9 mil. (see related story, T&G-1). Turning to the length of time FDA has taken to issue regulations, Glenn asked if delays have been caused by layers of review higher in the Administration. Kessler again avoided pointing his finger at the hierarchy of the Administration, but said instead that the "problem lies . . . with the agency itself." Noting that his statement is "not a popular answer within the agency," Kessler said that when he came to FDA he found that no one had tracked and held responsibility for implementing regulations. One function of the deputy commissioner for policy -- a position Kessler is establishing -- will be "ensuring that new regulations are written and issued promptly," the commissioner said. Michael Taylor is expected to join the agency shortly in that post. Pharmaceutical Manufacturers Association President Gerald Mossinghoff testified that FDA should establish a tracking system so that the status of pending INDs and NDAs can be ascertained. A tracking system also will make it "possible to have better measures of [FDA reviewer] performance and to identify obstacles," Mossinghoff said. Noting that CDER "has made significant progress in tracking the IND and NDA workload," he urged that such efforts "be continued, enhanced and generalized to the biologics component of the agency."
Part D Discount Liability Coming Into Focus: CMS Releases Drug Cost Data
Newly released Medicare Part D data sheds light on the sales hit that branded pharmaceutical manufacturers will face when the coverage gap discount program gets under way in 2011
FDA Skin Infections Guidance Spurs Debate On Endpoint Relevance
FDA appears headed for a showdown with clinicians and the pharmaceutical industry over the proposed new clinical trial endpoints for acute bacterial skin and skin structure infections, the guidance's approach for justifying a non-inferiority margin and proposed changes in the types of patients that should be enrolled in trials
Shire Hopes To Sow Future Deals With $50M Venture Fund
Specialty drug maker Shire has quietly begun scouting deals with a brand-new $50 million venture fund, the latest of several in-house investment arms to launch with their parent company's pipelines, not profits, as the measure of their worth
Subject: NDA REVIEW RESOURCE MANAGEMENT/SCHEDULING SYSTEM IS UNDER CONSIDERATION BY FDA, COMMISSIONER KESSLER TELLS SEN. GLENN HEARING


The Press Gang was a constant threat throughout the 18th century. Baytown's residents used subterfuge and brawn to thwart the Navy's recruitment process. Celebrate triumph over adversity. Brings a fresh, unanticipated, taste.