Statistical Mechanics of Lattice Systems

This motivating textbook gives a friendly rigorous introduction to fundamental concepts in equilibrium statistical mechanics covering a selection of specific models including the CurieWeiss 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 MerminWagner and LeeYang theorems and develops from scratch such workhorses as correlation inequalities the cluster expansion PirogovSinai 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.