Statistical mechanics of disordered systems : a mathematical perspective
著者
書誌事項
Statistical mechanics of disordered systems : a mathematical perspective
（Cambridge series on statistical and probabilistic mathematics）
Cambridge University Press, 2011, c2006
- : paperback
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注記
"First published 2006, first paperback edition 2011"--T.p. verso
Includes bibliographical references (p. [297]-308) and index
内容説明・目次
内容説明
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.
目次
- 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.
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