Introduction to the Renormalization Group and to Critical Phenomena
Author | : Gérard Toulouse |
Publisher | : John Wiley & Sons |
Total Pages | : 206 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : |
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Author | : Gérard Toulouse |
Publisher | : John Wiley & Sons |
Total Pages | : 206 |
Release | : 1977 |
Genre | : Mathematics |
ISBN | : |
Author | : J. J. Binney |
Publisher | : Oxford University Press |
Total Pages | : 477 |
Release | : 1992-06-11 |
Genre | : Science |
ISBN | : 0191660566 |
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.
Author | : Pierre Pfeuty |
Publisher | : |
Total Pages | : 190 |
Release | : 1975 |
Genre | : Critical phenomena (Physics) |
ISBN | : |
Author | : R. J. Creswick |
Publisher | : |
Total Pages | : 0 |
Release | : 2016-06-24 |
Genre | : Renormalization (Physics) |
ISBN | : 9780486793450 |
This introduction to the renormalization group, an edited and corrected second edition, discusses examples from diverse areas of physics. Designed for a one-semester course for advanced graduate students, the treatment requires a solid background in classical mechanics, statistical mechanics, and quantum mechanics. The text begins with an examination of self-similarity and scale invariance, followed by chapters on the renormalization group approaches to chaos and percolation, renormalization group and critical phenomena, and an extensive treatment of the Ising model. Additional topics include mean field theory and the Gaussian fixed point, the spherical model and the 1/n expansion, the two-dimensional X-Y model and the Kosterlitz-Thouless transition, and other subjects. Each chapter is augmented by problems and references, and three helpful Appendixes supplement the text. AUTHOR: R. J. Creswick is Professor in the Department of Physics and Astronomy, University of South Carolina.
Author | : Roland Bauerschmidt |
Publisher | : Springer Nature |
Total Pages | : 283 |
Release | : 2019-10-16 |
Genre | : Science |
ISBN | : 9813295937 |
This is a primer on a mathematically rigorous renormalisation group theory, presenting mathematical techniques fundamental to renormalisation group analysis such as Gaussian integration, perturbative renormalisation and the stable manifold theorem. It also provides an overview of fundamental models in statistical mechanics with critical behaviour, including the Ising and φ4 models and the self-avoiding walk. The book begins with critical behaviour and its basic discussion in statistical mechanics models, and subsequently explores perturbative and non-perturbative analysis in the renormalisation group. Lastly it discusses the relation of these topics to the self-avoiding walk and supersymmetry. Including exercises in each chapter to help readers deepen their understanding, it is a valuable resource for mathematicians and mathematical physicists wanting to learn renormalisation group theory.
Author | : James Binney |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : Critical phenomena (Physics) |
ISBN | : 9781383022605 |
A basic introduction to the theory of continuous phase transitions. The book provides a self-contained introduction to techniques that play important roles in contemporary physics for beginning graduate students.
Author | : Richard J. Creswick |
Publisher | : Wiley-Interscience |
Total Pages | : 432 |
Release | : 1992 |
Genre | : Science |
ISBN | : |
The renormalization group (RG) method has found applications in many areas of physics. The authors present simple RG treatments of such diverse problems as random walks, percolation, chaos and critical phenomena. Detailed introductory materials are presented in each area which makes it reasonably self–contained. The concepts of self–similarity and scale invariance are a common thread tying these problems together. Emphasis is placed on intuitive real–space RG calculations rather than formalism. The momentum–space RG is introduced and the 1/n and epsis expansions are discussed. A brief explanation of the field–theoretic approach to the RG serves as an introduction to more advanced techniques.
Author | : Dimo I. Uzunov |
Publisher | : World Scientific |
Total Pages | : 701 |
Release | : 2010 |
Genre | : Science |
ISBN | : 9814299499 |
This book provides a comprehensive introduction to the theory of phase transitions and critical phenomena. The content covers a period of more than 100 years of theoretical research of condensed matter phases and phase transitions providing a clear interrelationship with experimental problems. It starts from certain basic University knowledge of thermodynamics, statistical physics and quantum mechanics. The text is illustrated with classic examples of phase transitions. Various types of phase transition and (multi)critical points are introduced and explained. The classic aspects of the theory are naturally related with the modern developments. This interrelationship and the field-theoretical renormalization group method are presented in details. The main applications of the renormalization group methods are presented. Special attention is paid to the description of quantum phase transitions. This edition contains a more detailed presentation of the renormalization group method and its applications to particular systems.
Author | : Peter Kopietz |
Publisher | : Springer |
Total Pages | : 383 |
Release | : 2010-04-22 |
Genre | : Science |
ISBN | : 3642050948 |
The renormalization group (RG) has nowadays achieved the status of a meta-theory, which is a theory about theories. The theory of the RG consists of a set of concepts and methods which can be used to understand phenomena in many different ?elds of physics, ranging from quantum ?eld theory over classical statistical mechanics to nonequilibrium phenomena. RG methods are particularly useful to understand phenomena where ?uctuations involving many different length or time scales lead to the emergence of new collective behavior in complex many-body systems. In view of the diversity of ?elds where RG methods have been successfully applied, it is not surprising that a variety of apparently different implementations of the RG idea have been proposed. Unfortunately, this makes it somewhat dif?cult for beginners to learn this technique. For example, the ?eld-theoretical formulation of the RG idea looks at the ?rst sight rather different from the RG approach pioneered by Wilson, the latter being based on the concept of the effective action which is ite- tively calculated by successive elimination of the high-energy degrees of freedom. Moreover, the Wilsonian RG idea has been implemented in many different ways, depending on the particular problem at hand, and there seems to be no canonical way of setting up the RG procedure for a given problem.