TY  - BOOK
AU  - Bovier,Anton
TI  - Statistical mechanics of disordered systems: a mathematical perspective 
T2  - Cambridge series on statistical and probabilistic mathematics
SN  - 9780511616808 (ebook)
AV  - QC174.8 .B67 2006
U1  - 519.5 22
PY  - 2006///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Statistical mechanics
KW  - Mathematical statistics
KW  - Probabilities
KW  - System theory
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Principles of statistical mechanics -- Lattice gases and spin systems -- Gibbsian formalism for lattice spin systems -- Cluster expansions -- Gibbsian formalism and metastates -- The random-field Ising model -- Disordered mean-field models -- The random energy model -- Derrida's generalized random energy models -- The SK models and the Parisi solution -- Hopfield models -- The number partitioning problem
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511616808
ER  -