Introduction to the Replica Theory of Disordered Statistical Systems

Introduction to the Replica Theory of Disordered Statistical Systems

by Viktor Dotsenko
Pub. Date:
Cambridge University Press


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Introduction to the Replica Theory of Disordered Statistical Systems

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: 9780521021258
Publisher: Cambridge University Press
Publication date: 07/28/2005
Series: Collection Alea-Saclay: Monographs and Texts in Statistical Physics Series
Pages: 236
Product dimensions: 6.85(w) x 9.72(h) x 0.51(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.

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