Elements of Phase Transitions and Critical Phenomena: (Oxford Graduate Texts)

This is an open access title available under the terms of a CC BY-NC-ND 4.0 International licence. It is free to read on the Oxford Academic platform and offered as a free PDF download from OUP and selected open access locations. As an introductory account of the theory of phase transitions and critical phenomena, this book reflects lectures given by the authors to graduate students at their departments and is thus classroom-tested to help beginners enter the field. Most parts are written as self-contained units and every new concept or calculation is explained in detail without assuming prior knowledge of the subject. The book significantly enhances and revises a Japanese version which is a bestseller in the Japanese market and is considered a standard textbook in the field. It contains new pedagogical presentations of field theory methods, including a chapter on conformal field theory, and various modern developments hard to find in a single textbook on phase transitions. Exercises are presented as the topics develop, with solutions found at the end of the book, making the text useful for self-teaching, as well as for classroom learning.

Table of Contents:
1: Phase transitions and critical phenomena 2: Mean-field theories 3: Renormalization group and scaling 4: Implementation of the renormalization group 5: Field theory 6: Conformal field theory 7: Kosterlitz-Thouless transition 8: Random systems 9: Exact solutions and related topics 10: Duality 11: Numerical methods Appendix: Solutions to exercises

About the Author :
After spending three years as a postdoctoral fellow at Carnegie-Mellon University and Rutgers University in the US, Hidetoshi Nishimori returned to Japan, first as a research associate at Tokyo Institute of Technology. He is now a professor of physics at the same Institute. He received the Nishina Memorial Prize in 2006 for his work on spin glasses. He is a Fellow of the Institute of Physics. After receiving his PhD in Theoretical Physics at the Swiss Federal Institute of Technology, Gerardo Ortiz continued his career in the US, first as a postdoctoral fellow in the University of Illinois at Urbana-Champaign, and then as an Oppenheimer fellow at the Los Alamos National Laboratory ,where he stayed as a permanent staff member until 2006. He is currently professor of Physics at Indiana University, Bloomington. He is a Fellow of the Institute of Physics.

Review :
`The strengths of this book are the quality and experience of Nishimori and Ortiz as researchers and teachers. They know well how to explain physical theories and formalisms, and their writings have a very low threshold for the interested and mathematically inclined reader. The book has a very nice selection of topics, ranging from the basics in the theory of classical spin systems, via renormalization group theory and conformal field theory, to duality arguments and disordered systems. Above all, the authors have succeeded brilliantly in conveying the elegance of this particular field of mathematical physics.' Anthony Coolen, King's College London `I am convinced that this book will be extremely useful to students. It proposes a rather broad choice of topics, which have been wisely selected. It covers the standard theory of phase transitions without entering too much into the field theoretic technicalities, but insisting on precise examples (like the Kosterlitz-Thouless transition), and conceptual issues. I think that this book is likely to be a very valuable one, the kind of book that will immediately become a classic book, necessary to any graduate student willing to have a good knowledge in statistical physics.' Marc Mézard, Université de Paris Sud, Orsay, France `This book gives a comprehensive and readable introduction to the most important aspects of the modern theory of critical phenomena. After a thorough discussion of the basic approaches of mean field theory and the renormalization group, more advanced topics, such as conformal field theory and spin glasses, are discussed to a level from which the reader can proceed to more advanced texts. The subject matter is well illustrated by examples and exercises, which makes this an ideal graduate text as well as useful background material for the more casual reader.' John Cardy FRS, University of Oxford