pt. 1. General theory and basic examples -- pt. 2. Markov chains and Gauss fields as Gibbs measures -- pt. 3. Shift-invariant Gibbs measures -- pt. 4. Phase transitions in reflection positive models
Summary
"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians."Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area
