Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction
Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction
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DOI：
10.1017/9781316882603
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发表时间：
2017-11
期刊：
影响因子：
--
通讯作者：
S. Friedli;Y. Velenik
中科院分区：
文献类型：
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作者：
S. Friedli;Y. Velenik
这本激励性的教科书对平衡统计力学的基本概念进行了友好，严格的介绍，涵盖了特定模型的选择，包括Curie-Weiss和Ising模型，高斯自由场，O（n）模型和Kać相互作用模型。使用经典的概念，如吉布斯措施，压力，自由能，和熵，这本书暴露的主要特点的经典描述的大型系统的平衡，特别是中心问题的相变。它对待这样的重要议题，如佩尔斯的论点，Dobrushin唯一性，Mermin-Wagner和李-杨定理，并从零开始发展相关不等式，集群扩张，Pirogov西奈理论和反射积极性等主力。作为一个独立的课程编写的高年级本科生或开始研究生，详细的解释，大量的练习（与解决方案），并附录的数学结果和概念也使它成为一个方便的参考研究人员在相关领域。
This motivating textbook gives a friendly, rigorous introduction to fundamental concepts in equilibrium statistical mechanics, covering a selection of specific models, including the Curie-Weiss and Ising models, the Gaussian free field, O (n) models, and models with Kać interactions. Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin-Wagner and Lee-Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov-Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.