Statistical Mechanics of Disordered Systems

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Sprache: Englisch

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Beschreibung

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.

Inhaltsverzeichnis

Preface; Part I. Statistical Mechanics: 1. Introduction; 2. Principles of statistical mechanics; 3. Lattice gases and spin systems; 4. Gibbsian formalism; 5. Cluster expansions; Part II. Disordered Systems: Lattice Models: 6. Gibbsian formalism and metastates; 7. The random field Ising model; Part III: Disordered Systems: Mean Field Models: 8. Disordered mean field models; 9. The random energy model; 10. Derrida's generalised random energy models; 11. The SK models and the Parisi solution; 12. Hopfield models; 13. The number partitioning problem; Bibliography; Index of notation; Index.

Details

Erscheinungsjahr:	2012
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
ISBN-13:	9781107405332
ISBN-10:	1107405335
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Bovier, Anton
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	254 x 178 x 18 mm
Von/Mit:	Anton Bovier
Erscheinungsdatum:	20.03.2012
Gewicht:	0,619 kg