Preface; Convention; 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 Zd; 9. Models with continuous symmetry; 10. Reflection positivity; A. Notes; B. Mathematical appendices; C. Solutions to exercises; Bibliography; Index.
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Sacha Friedli is Associate Professor of Mathematics at the Universidade Federal de Minas Gerais, Brazil. His current research interests are in statistical mechanics, mathematical physics, and Markov processes. Yvan Velenik is Professor of Mathematics at the Université de Genève. His current work focuses on applications of probability theory to the study of classical statistical mechanics, especially lattice random fields and random walks.
'Rigorous Statistical Mechanics has a long tradition, starting in
the 1960s with Dobrushin, Lanford, Ruelle, Sinai and many other
mathematical physicists. Yet, surprisingly, there has not been an
up-to-date textbook on an introductory level. This gap is bridged
masterly by the present book. It addresses the curious newcomer by
employing a carefully designed structure, which starts from a
physics introduction and then uses the two-dimensional Ising model
as a stepping-stone towards the richness of the subject. The book
will be enjoyed by students and researchers with an interest in
either theoretical condensed matter physics or probability theory.'
Herbert Spohn, Technische Universität München
'An excellent introduction to classical equilibrium statistical
mechanics. There is clear concern with the understanding of ideas
and concepts behind the various tools and models. Topics are
presented through examples, making this book a genuine 'concrete
mathematical introduction'. While reading it, my first wish was to
use it as soon as possible in a course. It is a 'must' for the
libraries of graduate programs in mathematics or mathematical
physics.' Maria Eulália Vares, Universidade Federal do Rio de
Janeiro
'This book is a marvelous introduction to equilibrium statistical
mechanics for mathematically inclined readers, which does not
sacrifice clarity in the pursuit of mathematical rigor. The book
starts with basic definitions and a crash course in thermodynamics,
and gets to sophisticated topics such as cluster expansions, the
Pirogov-Sinai theory and infinite volume Gibbs measures through the
discussion of concrete models. This book should be on the bookshelf
of any serious student, researcher and teacher of mathematical
statistical mechanics.' Ofer Zeitouni, Weizmann Institute,
Israel
'Sacha Friedli and Yvan Velenik have succeeded in writing a unique,
modern treatise on equilibrium statistical mechanics. They cover
many fundamental concepts, techniques and examples in a didactic
manner, providing a remarkable source of knowledge, grounded and
refined by years of experience. Stimulating and appealing, this
book is likely to inspire generations of students and scientists.'
Francis Comets, Université Paris Diderot
'The authors have created an impressive book that shows its
strengths in several ways: thoughtful organization and a
well-designed presentation, real attention to the needs of the
reader, and a very nice guide to the existing literature. It could
be a model of how mathematical physics should be presented.' Bill
Satzer, MAA Reviews
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