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Introduction to the Replica Theory of Disordered Statistical Systems

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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.
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Editorial Reviews

Booknews
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)
From the Publisher
"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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Product Details

Table of Contents

Preface
1 Introduction 1
Pt. 1 Spin-glass systems 13
2 Physics of the spin-glass state 15
3 Mean-field theory of spin glasses 26
4 Physics of replica symmetry breaking 46
5 Ultrametricity 54
6 Experiments 64
Pt. 2 Critical phenomena and quenched disorder 75
7 Scaling theory of the critical phenomena 77
8 Critical phenomena in systems with disorder 97
9 Spin-glass effects in the critical phenomena 107
10 Two-dimensional Ising model with disorder 128
Pt. 3 Other types of disordered system 151
11 Ising systems with quenched random fields 153
12 One-dimensional directed polymers in random potentials 164
13 Vector breaking of replica symmetry 178
14 Conclusions 209
Bibliography 213
Index 219
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