Statistical Mechanics of Disordered Systems

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.