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Contemporary Physics

Critical point phenomena

B. L. Smith

Published Jul 1, 1969• 16 citations
Publisher

Abstract

During the last decade considerable effort has been expended in the study of critical phenomena. These investigations are especially rewarding because they provide important links between several diverse branches of physics. For example, antiferromagnets, pure fluids, binary solutions and alloys all exhibit analogous critical behaviour. It is now firmly established that the classical phenomenological theories that have been proposed to describe these systems fail in the critical region: mainly because they do not account for the fluctuation phenomena which occur close to critical points, and are a poor approximation for systems with shortrange forces. Considerable progress has been made in formulating more realistic models, for example the king and Heisenberg ferromegnets, and some success has been achieved in obtaining solutions for these models. Similar theories may be postulated to describe the critical behaviour of other systems. Recent progress in theoretical understanding and refinement of experimental techniques have helped to stimulate interest in the subject, and today the study of critical phenomena is one of the most promising and rapidly advancing areas of physics.

DOI
10.1080/00107516908204791

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During the last decade considerable effort has been expended in the study of critical phenomena. These investigations are especially rewarding because they provide important links between several diverse branches of physics. For example, antiferromagnets, pure fluids, binary solutions and alloys all exhibit analogous critical behaviour. It is now firmly established that the classical phenomenological theories that have been proposed to describe these systems fail in the critical region: mainly because they do not account for the fluctuation phenomena which occur close to critical points, and are a poor approximation for systems with shortrange forces. Considerable progress has been made in formulating more realistic models, for example the king and Heisenberg ferromegnets, and some success has been achieved in obtaining solutions for these models. Similar theories may be postulated to describe the critical behaviour of other systems. Recent progress in theoretical understanding and refinement of experimental techniques have helped to stimulate interest in the subject, and today the study of critical phenomena is one of the most promising and rapidly advancing areas of physics.
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.
The examination of phase transitions and critical phenomena has dominated statistical physics for the latter half of this century--there is a great theoretical challenge in solving special statistical mechanical models. Additionally, beautiful experimental results have elucidated the singularities (critical behavior) that occur in phase transitions. Although a few spectacular successes in the exact solution of simple models have occurred, interesting systems have mostly proven to be intractable from the analytic perspective. Because many physically disparate systems show identical critical behavior, identifying and understanding general principles of universality and their relationship to microscopic symmetries are of fundamental importance
The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was 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. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulation
Abstract The successful calculation of critical exponents for continuous phase transitions is one of the main achievements of theoretical physics over the last quarter-century. This was 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. Continuous phase transitions are introduced, then the necessary statistical mechanics is summarized, followed by standard models, some exact solutions and techniques for numerical simulations. The real-space renormalization group and mean-field theory are then explained and illustrated. The final chapters 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.
An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points of magnets, binary alloys, and fluids. Yet a multitude of related phenomena are mentioned. The most important distinct surface universality classes that may occur for a given universality class of bulk critical behavior are described, and the respective boundary conditions of the associated field theories are discussed. The short-distance singularities of the order-parameter profile in the diverse asymptotic regimes are surveyed.