A Modern Approach to Critical Phenomena
Igor Herbut
Cambridge University Press
The studies of the critical behaviors for a system near its phasetransition point constitutes an important subfield of theresearches in statistical mechanics and condensed matter physics.It has acquired a renewed interest due to the discovery of quantumcritical behaviors in correlated electron systems. The developmentof the theory of critical phenomena has a tremendous impact onboth statistical mechanics and quantum field theory, and theassociated renormalization group idea has now become a basiclanguage in thinking about many fundamental problems in condensedmatter physics. No wonder that there exist many books in themarket which address this issue. Among them, I have to mention theclassic book by S. K. Ma and the more recent little, butrefreshingly clear, book by John Cardy. There is also anoverwhelming monograph by J. Zinn-Justin. In my opinion, IgorHerbut's book stands out from its pedagogy and its modern flavors.To be more precise, although the contents of this book is, by itsvery nature, challenging, this book is accessible to any motivatedgraduate students with a solid background in quantum mechanics andstatistical mechanics. Moreover, unlike some old monographs, thisbook not only teach you the phi-4 theory, but also contains nicediscussions of the superconducting transition, the nonliear-sigmamodel, the KT transition, and the charge-vortex duality. In theend of the book, it gives the readers a brief but usefuldiscussion of the quantum phase transition. On the technical side,this book is devoted almost exclusively to the momentum-shell RGapproach which is a powerful tool and it is still widely used inthe research literature. However, I would like to recommend theuninitiated readers to read this book in companion with a standardfield theory textbook, such as chapter 10-13 of Peskin's book, tolearn some different perspectives on the renormalization group, inparticular, the Callen-Symanzik equation and the related stuff.As far as I can tell, the only missing "standard" topic in thisbook about the critical phenomena is a systematic discussion ofthe large-N calculation of the critical exponent. In the meantime, since most of the book is devoted to the classical phasetransitions, this book deals exclusively with bosonic fieldtheories. The author may like to consider to add more discussionsabout critical properties of fermonic systems or even thefermion-gauge coupled systems in the chapter about quantum phasetransition (in the 2nd edition?) of this book. Of course, nobodypromise you a rose garden. As a whole, this book serves as auseful reference to bridge the gap between the usual graduatecourse and the research literature. After reading this book, thestudent can go on studying the more specialized monograph, such asSachdev's book, and more importantly, starting doing their ownresearch works. I highly recommend this book to anyone interestedin the field theoretical approach to condensed matter physics.