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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
|---|---|---|---|---|---|
Searching... | 30000010345622 | QC174.8 B685 2006 | Open Access Book | Book | Searching... |
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Summary
Summary
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, 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 |
