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Statistical mechanics of disordered systems : = a mathematical perspective /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Statistical mechanics of disordered systems :/ Anton Bovier.
Reminder of title:	a mathematical perspective /
Author:	Bovier, Anton,
Description:	1 online resource (xiv, 312 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Statistical mechanics. -
Online resource:	https://doi.org/10.1017/CBO9780511616808
ISBN:	9780511616808 (ebook)

Statistical mechanics of disordered systems : = a mathematical perspective /
Bovier, Anton,1957-

Statistical mechanics of disordered systems :a mathematical perspective /Anton Bovier. - 1 online resource (xiv, 312 pages) :digital, PDF file(s). - Cambridge series on statistical and probabilistic mathematics ;18. - Cambridge series on statistical and probabilistic mathematics ;32..

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.

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.

ISBN: 9780511616808 (ebook)Subjects--Topical Terms:

676754
Statistical mechanics.

LC Class. No.: QC174.8 / .B67 2006

Dewey Class. No.: 519.5

Statistical mechanics of disordered systems : = a mathematical perspective /
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500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Statistical mechanics. $3 676754
650 0 $a Mathematical statistics. $3 527941
650 0 $a Probabilities. $3 527847
650 0 $a System theory. $3 566168
776 0 8 $i Print version: $z 9780521849913
830 0 $a Cambridge series on statistical and probabilistic mathematics ; $v 32. $3 1133567
856 4 0 $u https://doi.org/10.1017/CBO9780511616808