Автор: Sacha Friedli, Yvan Velenik
Название: Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction
Издательство: Cambridge University Press
Год: 2017
ISBN: 1107184827
Язык: English
Формат: pdf
Размер: 11,2 mb
Страниц: 628

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.