Advanced Statistical Mechanics (Hardcover)

Barry M McCoy

Advanced Statistical Mechanics (Hardcover)
  • 出版商: Oxford University
  • 出版日期: 2010-02-28
  • 售價: $1,800
  • 貴賓價: 9.8 折 $1,764
  • 語言: 英文
  • 頁數: 640
  • 裝訂: Hardcover
  • ISBN: 0199556636
  • ISBN-13: 9780199556632

    • 立即出貨 (庫存=1)

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商品描述

Self contained summary of advances in statistical mechanics in the last fifty years
*Detailed historical chronologies of the development of all topics treated
*Many exactly solved nontrivial problems done in detail
*Many open problems and conjectures presented
*Extensive use of computer results to obtain analytic insight

Statistical Mechanics is the study of systems where the number of interacting particles becomes infinite. In the last fifty years tremendous advances have been made which have required the invention of entirely new fields of mathematics such as quantum groups and affine Lie algebras. They have engendered remarkable discoveries concerning non-linear differential equations and algebraic geometry, and have produced profound insights in both condensed matter physics and quantum field theory. Unfortunately, none of these advances are taught in graduate courses in statistical mechanics.

This book is an attempt to correct this problem. It begins with theorems on the existence (and lack) of order for crystals and magnets and with the theory of critical phenomena, and continues by presenting the methods and results of fifty years of analytic and computer computations of phase transitions. It concludes with an extensive presentation of four of the most important of exactly solved problems: the Ising, 8 vertex, hard hexagon and chiral Potts models.

Table Of Contents

1: Basic Principles

2: Reductionism, Phenomena and Models

3: Stability, Existence and Uniqueness

4: Theorems on Order

5: Critical Phenomena and Scaling Theory

6: Mayer Virial Expansions and Groenevelt's Theorems

7: Ree-Hoover Virial Expansion and Hard Spheres

8: High Density Expansions

9: High Temperature Expansions for Magnets at H=0

10: The Ising Model in Two Dimensions; Summary of Results

11: The Pfaffian Solution of the Ising Model

12: Ising Model Spontaneous Magnetization, Form Factors and Susceptibility

13: The Star-Triangle (Yang-Baxter) Equation

14: The Eight Vertex and XYZ models

15: The RSOS and the Chiral Potts models

16: Conclusion

商品描述(中文翻譯)

這本書是對過去五十年統計力學進展的自成一體的摘要。它詳細記錄了所有涉及主題的發展的歷史時間表，並詳細解決了許多非平凡的問題。同時也提出了許多未解決的問題和猜想。書中廣泛使用計算機結果來獲得分析洞察力。

統計力學是研究粒子數目無限增加的系統的學科。在過去五十年中，取得了巨大的進展，這些進展需要創造全新的數學領域，如量子群和仿射李代數。它們引發了關於非線性微分方程和代數幾何的重大發現，並在凝聚態物理和量子場論中產生了深刻的洞察力。不幸的是，這些進展在統計力學的研究生課程中並未教授。

這本書試圖解決這個問題。它從關於晶體和磁體的有序性（或無序性）的定理以及臨界現象的理論開始，並繼續介紹五十年來相變的分析和計算方法和結果。最後，它詳細介紹了四個最重要的確切解決問題：伊辛模型、8頂點模型、硬六角模型和手性波茨模型。

目錄：

1：基本原理
2：還原主義、現象和模型
3：穩定性、存在性和唯一性
4：有序性的定理
5：臨界現象和尺度理論
6：梅爾-維里爾展開和格羅尼維爾定理
7：里-胡佛展開和硬球
8：高密度展開
9：H=0時磁體的高溫展開
10：二維伊辛模型；結果摘要
11：伊辛模型的帕菲安解
12：伊辛模型的自發磁化、形狀因子和磁化率
13：星-三角（楊-巴克斯特）方程
14：八頂點和XYZ模型
15：RSOS和手性波茨模型
16：結論

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