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libcats.org
A Modern Approach to Critical PhenomenaIgor HerbutThe studies of the critical behaviors for a system near its phase
transition point constitutes an important subfield of the researches in statistical mechanics and condensed matter physics. It has acquired a renewed interest due to the discovery of quantum critical behaviors in correlated electron systems. The development of the theory of critical phenomena has a tremendous impact on both statistical mechanics and quantum field theory, and the associated renormalization group idea has now become a basic language in thinking about many fundamental problems in condensed matter physics. No wonder that there exist many books in the market which address this issue. Among them, I have to mention the classic book by S. K. Ma and the more recent little, but refreshingly clear, book by John Cardy. There is also an overwhelming monograph by J. Zinn-Justin. In my opinion, Igor Herbut's book stands out from its pedagogy and its modern flavors. To be more precise, although the contents of this book is, by its very nature, challenging, this book is accessible to any motivated graduate students with a solid background in quantum mechanics and statistical mechanics. Moreover, unlike some old monographs, this book not only teach you the phi-4 theory, but also contains nice discussions of the superconducting transition, the nonliear-sigma model, the KT transition, and the charge-vortex duality. In the end of the book, it gives the readers a brief but useful discussion of the quantum phase transition. On the technical side, this book is devoted almost exclusively to the momentum-shell RG approach which is a powerful tool and it is still widely used in the research literature. However, I would like to recommend the uninitiated readers to read this book in companion with a standard field theory textbook, such as chapter 10-13 of Peskin's book, to learn some different perspectives on the renormalization group, in particular, the Callen-Symanzik equation and the related stuff. As far as I can tell, the only missing "standard" topic in this book about the critical phenomena is a systematic discussion of the large-N calculation of the critical exponent. In the mean time, since most of the book is devoted to the classical phase transitions, this book deals exclusively with bosonic field theories. The author may like to consider to add more discussions about critical properties of fermonic systems or even the fermion-gauge coupled systems in the chapter about quantum phase transition (in the 2nd edition?) of this book. Of course, nobody promise you a rose garden. As a whole, this book serves as a useful reference to bridge the gap between the usual graduate course and the research literature. After reading this book, the student can go on studying the more specialized monograph, such as Sachdev's book, and more importantly, starting doing their own research works. I highly recommend this book to anyone interested in the field theoretical approach to condensed matter physics. Ссылка удалена правообладателем ---- The book removed at the request of the copyright holder.
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