Statistical Mechanics of Disordered Systems
A Mathematical Perspective
Erschienen am 19. Juli 2012
Buch
Softcover
328 Seiten
978-1-107-40533-2 (ISBN)
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.
Rezensionen / Stimmen
'... a graduate-level introduction for mathematicians and physicists 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 some basic knowledge of classical physics; on the mathematics side, the reader should have a good working knowledge of graduate level probability theory.' L'enseignement mathematique 'Bovier's book contains a huge amount of material on statistical mechanics of disordered systems, arranged in a coherent way. The results are fascinating and the mathematics beautiful and deep. The wealth of ideas is enormous. This book constitutes a very complete and comprehensive treatise on the analysis of disordered systems. It is an indispensable reference in the field and it is suitable as well for advanced graduate courses. There is no doubt that this book will be influential.' MathSciNet '...the value and usefulness of the book by A. Bovier for anyone interested in the rigourous theory of disordered (spin) systems can be hardly overestimated.' Journal of Statistical PhysicsWeitere Details
Reihe
Sprache
Englisch
Verlagsort
Cambridge
Großbritannien
Zielgruppe
Für Beruf und Forschung
Produkt-Hinweis
Broschur/Paperback
Maße
Höhe: 254 mm
Breite: 178 mm
Dicke: 18 mm
Gewicht
619 gr
ISBN-13
978-1-107-40533-2 (9781107405332)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
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Person
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.
Inhalt
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.