Statistical Mechanics of Disordered Systems: A Mathematical Perspective

✍ Scribed by Anton Bovier

• Book ID: 127447278
• Publisher: Cambridge University Press
• Year: 2006
• Tongue: English
• Weight: 4 MB
• Series: Cambridge Series in Statistical and Probabilistic Mathematics
• Category: Library
• ISBN: 0511169116

✦ Synopsis

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.