Phase Transitions in the Theory of Lattice Gases

Erscheinungsjahr 2025
ISBN: 978-1-108-49185-3
Verlag: Cambridge University Press

Buch, Englisch, Band 52, 640 Seiten

Reihe: New Mathematical Monographs

The intersection of statistical mechanics and mathematical analysis has proved a fertile ground for mathematical physics and probability, and in the decades since lattice gases were first proposed as a model for describing physical systems at the atomic level, our understanding of them has grown tremendously. A book that provides a comprehensive account of the methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models has been long overdue. This book, written by one of the masters of the subject, is just that. Topics covered include correlation inequalities, Lee-Yang theorems, the Peierls method, the Hohenberg-Mermin-Wagner method, infrared bounds, random cluster methods, random current methods and BKT transition. The final section outlines major open problems to inspire future work. This is a must-have reference for researchers in mathematical physics and probability and serves as an entry point, albeit advanced, for students entering this active area.

Autoren/Hrsg.

Simon, Barry

Inhaltsverzeichnis

Notation; 1. A framework for lattice gases; 2. Correlation inequalities; 3. The Lee-Yang theorem; 4. Peierls argument; 5. No continuous symmetry breaking in 2D (and other situations); 6. Infrared bounds; 7. Stochastic geometric representations; 8. Berezinskii-Kosterlitz-Thouless transition; 9. Final thoughts; References; Author index; Subject index.

Über Autor(innen)

Simon, Barry
Barry Simon is a mathematical physicist who has served on the faculty of Princeton and Caltech. Noted for his many books and research contributions, his honours include the AMS Steele Prize for Lifetime Achievement and the APS Heineman Prize in Mathematical Physics.