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    Statistical Mechanics of Disordered Systems: A Mathematical Perspective (Cambridge Series in Statistical and Probabilistic Mathematic) (Hardback) By (author) Anton Bovier, Series edited by R. Gill, Series edited by Brian D. Ripley, Series edited by S. Ross, Series edited by B.W. Silverman, Series edited by M. Stein

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    DescriptionFirst published in 2006, 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.


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  • Full bibliographic data for Statistical Mechanics of Disordered Systems

    Title
    Statistical Mechanics of Disordered Systems
    Subtitle
    A Mathematical Perspective
    Authors and contributors
    By (author) Anton Bovier, Series edited by R. Gill, Series edited by Brian D. Ripley, Series edited by S. Ross, Series edited by B.W. Silverman, Series edited by M. Stein
    Physical properties
    Format: Hardback
    Number of pages: 324
    Width: 179 mm
    Height: 254 mm
    Thickness: 20 mm
    Weight: 806 g
    Language
    English
    ISBN
    ISBN 13: 9780521849913
    ISBN 10: 0521849918
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 03
    LC subject heading:
    BIC subject category V2: PB
    LC subject heading:
    BIC subject category V2: PHS
    LC subject heading:
    DC22: 519.5
    B&T General Subject: 710
    Warengruppen-Systematik des deutschen Buchhandels: 16200
    B&T Modifier: Academic Level: 02
    Ingram Subject Code: MA
    Libri: I-MA
    B&T Modifier: Text Format: 06
    LC subject heading: ,
    BISAC V2.8: MAT029000
    BIC subject category V2: PHFC, PBK
    B&T Merchandise Category: UP
    BISAC V2.8: MAT007000
    LC subject heading: ,
    LC classification: QC174.8 .B67 2006
    Thema V1.0: PB
    Edition statement
    New.
    Illustrations note
    30 figures
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    30 June 2006
    Publication City/Country
    Cambridge
    Author Information
    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.
    Review quote
    '... 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 Physics
    Table of contents
    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.