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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.

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Book Details

ISBN: 9780521849913
ISBN-10: 0521849918
Format: Hardback
(254mm x 178mm x 19mm)
Pages: 328
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 8-Jun-2006
Country of Publication: United Kingdom

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Author Biography - Anton Bovier

Professor Bovier is an active researcher, having published over 90 scientific papers, and is a frequently invited speaker at international meetings on probability and mathematics.

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