Gibbs Measures and Phase Transitions (eBook, PDF)

"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." Zentralblatt für Mathematik (review of the first edition)

"The book is an excellent basis for a serious study. It is carefully written, the proofs are detailed and clear, the examples are illuminating. Over 650 annotated references provide a useful orientation in the huge existing literature." Mathematical Reviews