Statistical Mechanics of Disordered Systems: A Mathematical Perspective

by Anton Bovier

• ISBN13: 9780521849913
• ISBN10: 0521849918
• Format: Hardcover
• Copyright: 2006-06-19
• Publisher: Cambridge University Press

Summary

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for mathematicians and for physicists interested in the mathematical foundations of the field, and can be used as a textbook for a two-semester course on mathematical statistical mechanics. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory. The book starts with a concise introduction to statistical mechanics, proceeds to disordered lattice spin systems, and concludes with a presentation of the latest developments in the mathematical understanding of mean-field spin glass models. In particular, recent progress towards a rigorous understanding of the replica symmetry-breaking solutions of the Sherrington-Kirkpatrick spin glass models, due to Guerra, Aizenman-Sims-Starr and Talagrand, is reviewed in some detail.

Table of Contents

Preface

Part I. Statistical Mechanics: 1. Introduction

2. Principles of statistical mechanics

3. Lattice gases and spin systems

4. Gibbsian formalism

5. Cluster expansions

Part II. Disordered Systems: Lattice Models: 6. Gibbsian formalism and metastates

7. The random field Ising model

Part III: Disordered Systems: Mean Field Models

8. Disordered mean field models

9. The random energy model

10. Derrida's generalised random energy models

11. The SK models and the Parisi solution

12. Hopfield models

13. The number partitioning problem

Bibliography

Index of notation

Index.