Phase Transitions in the Theory of Lattice Gases
Seiten
2025
Cambridge University Press (Verlag)
978-1-108-49185-3 (ISBN)
Cambridge University Press (Verlag)
978-1-108-49185-3 (ISBN)
This comprehensive text looks at methods used in the study of phase transitions for Ising models and classical and quantum Heisenberg models. Covering decades of research, it will serve as a reference for researchers and an entry point, albeit advanced, to students entering this active area.
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.
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.
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.
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.
| Erscheinungsdatum | 01.11.2025 |
|---|---|
| Reihe/Serie | New Mathematical Monographs |
| Zusatzinfo | Worked examples or Exercises |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 1470 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| Naturwissenschaften ► Physik / Astronomie ► Thermodynamik | |
| ISBN-10 | 1-108-49185-5 / 1108491855 |
| ISBN-13 | 978-1-108-49185-3 / 9781108491853 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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