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.

Review

'... a graduate-level introduction for mathematicians and physicists 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 some basic knowledge of classical physics; on the mathematics side, the reader should have a good working knowledge of graduate level probability theory.' L'enseignement mathematique

'Bovier's book contains a huge amount of material on statistical mechanics of disordered systems, arranged in a coherent way. The results are fascinating and the mathematics beautiful and deep. The wealth of ideas is enormous. This book constitutes a very complete and comprehensive treatise on the analysis of disordered systems. It is an indispensable reference in the field and it is suitable as well for advanced graduate courses. There is no doubt that this book will be influential.' MathSciNet

'...the value and usefulness of the book by A. Bovier for anyone interested in the rigourous theory of disordered (spin) systems can be hardly overestimated.' Journal of Statistical Physics

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