Statistical Mechanics of Disordered Systems
A Mathematical Perspective
Seiten
2012
Cambridge University Press (Verlag)
978-1-107-40533-2 (ISBN)
Cambridge University Press (Verlag)
978-1-107-40533-2 (ISBN)
A self-contained graduate-level introduction to the statistical mechanics of disordered systems. In three parts, the book treats basic statistical mechanics; disordered lattice spin systems; and latest developments in the mathematical understanding of mean-field spin glass models. It assumes basic knowledge of classical physics and working knowledge of graduate-level probability theory.
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.
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.
| Erscheint lt. Verlag | 19.7.2012 |
|---|---|
| Reihe/Serie | Cambridge Series in Statistical and Probabilistic Mathematics |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 570 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Statistik | |
| ISBN-10 | 1-107-40533-5 / 1107405335 |
| ISBN-13 | 978-1-107-40533-2 / 9781107405332 |
| Zustand | Neuware |
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