The Theory of Critical Phenomena

An Introduction to the Renormalization Group


J. J. Binney, N. J. Dowrick,

A. J. Fisher and M. E. J. Newman

The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last twenty-five years. It has been achieved through the use of scaling and field-theoretic techniques which have since become standard equipment in many areas of physics, especially quantum field theory. This book provides a thorough introduction to these techniques at a level suitable for beginning graduate students. The text assumes only a sound undergraduate background in physics and mathematics. In the first chapters of the book, continuous phase transitions are introduced, and then the necessary statistical mechanics is summarized, followed by an introduction to some of the standard models of phase transitions, some exact solutions, and techniques for numerical simulation. Next, mean-field theory and the real-space renormalization group are explained and illustrated. The last eight chapters of the book cover the Landau-Ginzburg model, from physical motivation, through diagrammatic perturbation theory and renormalization, to the renormalization group and the calculation of critical exponents above and below the critical temperature.


...a book which is exceptional in two essential respects: first, it covers, in a self-contained manner, practically all aspects of the subject; and second, it is comprehensible from the beginning to the end for students with only a good undergraduate background in physics; no knowledge of quantum field theory is needed for understanding even the most involved parts of the renormalization group theory.

The pedagogical level of this excellent textbook is very high. The reader will appreciate the frequent summaries throughout the book of main ideas as well as the arrangement of technical details and mathematical techniques in numerous boxes and appendices; this makes the book easily readable. Moreover, at the end of each chapter, several problems are given, with their complete solutions at the back of the book. In trying to solve them, the reader will learn whether he has profited from this wonderful book as much as he really should.

V. Dvorak, Condensed Matter News

A niche existed for a book in the important interface between the theory of critical phenomena and the technology of field theory. I say existed, because it has now been most admirably filled by this volume... The work throughout is reader-friendly, with frequent discussions of physical motivation, some historical background and interesting comments on the varying viewpoints of statistical and particle physicists.

...a book that can be unreservedly recommended to theoretical honours or starting graduate students; also to researchers who may be seeking to fill a void in their understanding in this area, which has marked some of the great advances in theoretical physics in recent decades.

M. J. Buckingham, University of Western Australia

...deserves a high rating. The book is written very clearly and simply, which makes it accessible to anyone who passed the principal undergraduate physics courses. Teachers and students either teaching or studying phase transistions - wherever they exist - should find this book very useful.

M. Gitterman, Bar-Ilan University, Israel.

About the authors:

James Binney and Nigel Dowrick are Fellows of Merton and St. John's Colleges respectively, at the University of Oxford, Andrew Fisher is on the physics faculty at University College, London, and Mark Newman at the Santa Fe Institute in Santa Fe, New Mexico.

The Theory of Critical Phenomena is published by
Oxford University Press.