1.

Record Nr.

UNINA9910823314703321

Autore

Bovier Anton <1957->

Titolo

Statistical mechanics of disordered systems : a mathematical perspective / / Anton Bovier

Pubbl/distr/stampa

Cambridge, UK, : Cambridge University Press, 2006

ISBN

1-107-15343-3

1-280-48005-X

9786610480050

0-511-16868-3

0-511-16911-6

0-511-16769-5

0-511-31455-8

0-511-61680-5

0-511-16823-3

Edizione

[1st ed.]

Descrizione fisica

1 online resource (xiv, 312 pages) : digital, PDF file(s)

Collana

Cambridge series in statistical and probabilistic mathematics ; ; [18]

Disciplina

519.5

Soggetti

Statistical mechanics

Mathematical statistics

Probabilities

System theory

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Nota di bibliografia

Includes bibliographical references (p. [297]-308) and index.

Nota di contenuto

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.

Sommario/riassunto

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.