Statistical Mechanics of Disordered Systems

A Mathematical Perspective
Erscheinungsjahr 2012
ISBN: 978-1-107-40533-2
Verlag: Cambridge University Press

Buch, Englisch, Band 18, 328 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 619 g

Reihe: Cambridge Series in Statistical and Probabilistic Mathematics

Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. 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, recent 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.

Autoren/Hrsg.

Bovier, Anton

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

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.

Über Autor(innen)

Bovier, Anton
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.