Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction

ISBN-13: 9781107184824 / Angielski / Twarda / 2017 / 640 str.

Sacha Friedli; Yvan Velenik

Opis

A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

Recenzje

'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

Spis treści

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.

O autorze

Friedli, Sacha
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. Velenik, Yvan
Yvan Velenik is Professor of Mathematics at the Université de Genève. His current work focuses on applications of probability theory to the study of classical statistical mechanics, especially lattice random fields and random walks.