Sacha Friedli

Statistical Mechanics of Lattice Systems (eBook, PDF)

A Concrete Mathematical Introduction

• Format: PDF

Produktbeschreibung

This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O(n) models, and models with Kac interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin-Wagner and Lee-Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov-Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 23. November 2017
• Englisch
• ISBN-13: 9781316886960
• Artikelnr.: 50215611

Autorenporträt

Sacha Friedli is Associate Professor of Mathematics at the Universidade Federal de Minas Gerais, Brazil. His current research interests are in statistical mechanics, mathematical physics, and Markov processes.

Inhaltsangabe

Preface; Convention; 1. Introduction; 2. The Curie-Weiss model; 3. The Ising model; 4. Liquid-vapor equilibrium; 5. Cluster expansion; 6. Infinite-volume Gibbs measures; 7. Pirogov-Sinai theory; 8. The Gaussian free field on Zd; 9. Models with continuous symmetry; 10. Reflection positivity; A. Notes; B. Mathematical appendices; C. Solutions to exercises; Bibliography; Index.

Rezensionen

'Rigorous Statistical Mechanics has a long tradition, starting in the 1960s with Dobrushin, Lanford, Ruelle, Sinai and many other mathematical physicists. Yet, surprisingly, there has not been an up-to-date textbook on an introductory level. This gap is bridged masterly by the present book. It addresses the curious newcomer by employing a carefully designed structure, which starts from a physics introduction and then uses the two-dimensional Ising model as a stepping-stone towards the richness of the subject. The book will be enjoyed by students and researchers with an interest in either theoretical condensed matter physics or probability theory.' Herbert Spohn, Technische Universität München