Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book gives a graduate-level introduction to the field. It 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. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory.
Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book gives a graduate-level introduction to the field. It 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. It assumes only basic knowledge of classical physics and, on the mathematics side, a good working knowledge of graduate-level probability theory.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
Inhaltsangabe
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.
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.
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