Introduction to the Replica Theory of Disordered Statistical Systems

by Viktor Dotsenko

Overview

This text describes the statistical mechanics of classical spin systems with quenched disorder. The first part covers the physics of spin-glass states using results obtained within the framework of the mean field theory of spin glasses. The second part is devoted to the theory of critical phenomena in the presence of weak quenched disorder. This includes a systematic derivation of the traditional renormalization group theory. In the third part Dotsenko describes other types of disordered systems, relating them to new results at the frontiers of modern research. The book is suitable for graduate students and researchers in the field of statistical mechanics of disordered systems.

Product Details

ISBN-13:	9780521773409
Publisher:	Cambridge University Press
Publication date:	11/02/2000
Series:	Collection Alea-Saclay: Monographs and Texts in Statistical Physics
Pages:	234
Product dimensions:	6.69(w) x 9.61(h) x 0.55(d)

Table of Contents

Preface; 1. Introduction; Part I. Spin-Glass Systems: 2. Physics of the spin glass state; 2. The mean-field theory of spin glasses; 4. Physics of replica symmetry breaking; 5. Ultrametricity; 6. Experiments; Part II. Critical Phenomena and Quenched Disorder: 7. Scaling theory of the critical phenomena; 8. Critical behaviour in systems with disorder; 9. Spin glass effects in the critical phenomena; 10. Two dimensional Ising model with disorder; Part III. Other Types of Disordered Systems: 11. Ising systems with quenched random fields; 12. One dimensional directed polymers in random potentials; 13. Vector breaking of replica symmetry; 14. Conclusions; References.

Editorial Reviews

For graduate students and researchers with a basic knowledge of theoretical physics and statistical mechanics, Dotsenko (theoretical physics, U. of Paris IV and Landau Institute for Theoretical Physics, Moscow) introduces the statistical mechanics of classical spin systems with quenched disorder. He first describes the physics of spin-glass states and the technique of replica symmetry breaking. Then he discusses the theory of critical phenomena in the presence of weak quenched disorder, and new research results concerning other types of disordered systems. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews

"The book's principal strength is that it provides a clear introduction to the mathematical machinery of RSB, accessible to an advanced graduate student interested in working in the statistical mechanics of disordered systems. For this reason alone it should be part of the library of any theorist working in these areas...an important contribution." Physics Today

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