Statistical Mechanics of Lattice Systems

A Concrete Mathematical Introduction

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• Publisher: Cambridge University Press
• Year: 2017
• ISBN:
  9781316886960
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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 Ka? 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.

Table of contents

• Cover
• Half-title page
• Title page
• Copyright page
• Dedication
• Contents
• Preface
• Conventions
• 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 Z[sup(d)]
• 9 Models with Continuous Symmetry
• 10 Reflection Positivity
• A Notes
• B Mathematical Appendices
• C Solutions to Exercises
• References
• Index