Statistical Mechanics of Disordered Systems: A Mathematical Perspective: 18 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 18)
Cambridge University Press
Edition: Illustrated, 6/8/2006
EAN 9780521849913, ISBN10: 0521849918
Hardcover, 328 pages, 25.4 x 17.8 x 2 cm
Language: English
Originally published in English
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.
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.