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Statistical Mechanics of Disordered Systems
A Mathematical Perspective

$51.99 (P)

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Author: Anton Bovier, Technische Universität Berlin and Weierstraβ-Institut für Angewandte Analysis und Stochastik
  • Date Published: July 2012
  • availability: Available
  • format: Paperback
  • isbn: 9781107405332

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About the Authors
  • 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.

    • Comprehensive introduction to an active and fascinating area of research
    • Clear exposition that builds to the state of the art in the mathematics of spin glasses
    • Written by a well-known and active researcher in the field
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    Reviews & endorsements

    "This book grew out of lecture notes and courses, and was prepared and polished over the last six years. Long-awaited, it is carefully prepared in a pedagogical style, with selected themes and progressive difficulty. It presents a broad overview of the field with modern tools and elaborate techniques, culminating with deep results and fascinating pictures. However, the author succeeds in also making it nice to read and easy to handle, keeping the style as direct as possible..."
    Francis Comets, Mathematical Reviews

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    Product details

    • Date Published: July 2012
    • format: Paperback
    • isbn: 9781107405332
    • length: 328 pages
    • dimensions: 254 x 178 x 17 mm
    • weight: 0.57kg
    • availability: Available
  • 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.

  • Author

    Anton Bovier, Technische Universität Berlin and Weierstraβ-Institut für Angewandte Analysis und Stochastik

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