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Physics Bulletin

Phase Transitions and Critical Phenomena Vol 1 Exact Results

E W Lee

Published Aug 1, 1973• 14 citations
Publisher

Abstract

C Domb and M S Green (eds) London: Academic Press 1972 pp xv + 506 price £10 The aim of this series of books is to present a coherent account of all that is definitely known about phase transition and critical phenomena. This first volume is devoted to the presentation of exact results in equilibrium statistical mechanics.
DOI
10.1088/0031-9112/24/8/022

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Critical phenomena

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•Dec 2, 2010•347 citations

Introduction to Phase Transitions and Critical Phenomena

D. J. Thouless

H E Stanley Oxford: University Press 1971 pp xx + 308 price £5 In the past fifteen years or so there has been a lot of experimental and theoretical work on the nature of critical phenomena in the neighbourhood of second order phase transitions. It has not been easy to get a good overall view of this work without digging through the rather complex original literature, although there are some good review articles covering particular aspects of the work.

Physics Bulletin•Apr 1, 1972•194 citations
C Domb and M S Green (eds) London and New York: Academic 1976 pp xvii + 420 price £13.50 The subject of phase transitions has rapidly advanced over the last decade and the volume under review is one of a series giving a comprehensive survey of both the theoretical and experimental aspects in this area. This volume contains an attractive article by Kadanoff on the main unifying ideas of universality and scaling (although the innocent reader should beware of misprints) and other contributions discuss mean field theory, applications of neutron scattering and mode coupling methods for discussing nonequilibrium behaviour near a critical point.
Abstract Phase transitions and critical phenomena have consistently been among the principal subjects of active studies in statistical physics. The simple act of transforming one state of matter or phase into another, for instance by changing the temperature, has always captivated the curious mind. This book provides an introductory account on the theory of phase transitions and critical phenomena, a subject now recognized to be indispensable for students and researchers from many fields of physics and related disciplines. The first five chapters are very basic and quintessential, and cover standard topics such as mean-field theories, the renormalization group and scaling, universality, and statistical field theory methods. The remaining chapters develop more advanced concepts, including conformal field theory, the Kosterlitz-Thouless transition, the effects of randomness, percolation, exactly solvable models, series expansions, duality transformations, and numerical techniques. Moreover, a comprehensive series of appendices expand and clarify several issues not developed in the main text. The important role played by symmetry and topology in understanding the competition between phases and the resulting emergent collective behaviour, giving rise to rigidity and soft elementary excitations, is stressed throughout the book. Serious attempts have been directed toward a self-contained modular approach so that the reader does not have to refer to other sources for supplementary information. Accordingly, most of the concepts and calculations are described in detail, sometimes with additional/auxiliary descriptions given in appendices and exercises. The latter are presented as the topics develop with solutions found at the end of the book, thus giving the text a self-learning character.