| Statistical Mechanics of Disordered Systems: A Mathematical Perspective Contributor(s): Bovier, Anton (Author), Gill, R. (Editor), Ripley, B. D. (Editor) |
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ISBN: 0521849918 ISBN-13: 9780521849913 Publisher: Cambridge University Press OUR PRICE: $97.85 Product Type: Hardcover Published: June 2006 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Differential Equations - General - Mathematics | Probability & Statistics - General |
| Dewey: 519.5 |
| LCCN: 2006297071 |
| Series: Cambridge Series in Statistical and Probabilistic Mathematic |
| Physical Information: 0.7" H x 6.6" W x 9.9" (1.70 lbs) 328 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
