Statistical Mechanics of Disordered Systems A Mathematical Perspective [Hardcover]

A self-contained graduate-level introduction to the statistical mechanics of disordered systems.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.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.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; 7lã#