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Statistical Mechanics of Lattice Systems : Volume 1: Closed-Form and Exact Solutions

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概要 This two-volume work provides a comprehensive study of the statistical mechanics of lattice models. It introduces the reader to the main areas in statistical mechanics and the theory of phase transiti...ons. The development is built on a firm mathematical and physical basis. Volume 1 contains an account of mean-field and cluster variation methods successfully used in many applications in solid-state physics and theoretical chemistry as well as an account of exact results for the Ising and six-vertex models and those derivable by transformation methods. Volume 2 includes extensive treatments of scaling theory, algebraic and real-space renormalization methods and the eight-vertex model. It also includes an account of series methods and a treatment of dimer assemblies.続きを見る
目次 1. Introduction to Thermodynamics and Phase Transitions
2. Statistical Mechanics and the One-Dimensional Ising Model
3. The Mean-Field Approximation, Scaling and Critical Exponents
4. Antiferromagnets and Other Magnetic Systems
5. Lattice Gases
6. Solid Mixtures and the Dilute Ising Model
7. Cluster Variation Methods
8. Exact Results for Two-Dimensional Ising Models
9. Applications of Transform Methods
10. The Six-Vertex Model
A. Appendices
A.1 Regular Lattices
A.2 Elliptic Integrals and Functions
A.2.1 Elliptic Integrals
A.2.2 Elliptic Functions
A.2.3 Results Required for Chapter 8
A.3 The Water Molecule and Hydrogen Bonding
A.4 Results for the Six-Vertex Model
A.4.1 The Proof of I
A.4.2 The Proof of II
A.4.3 The Proof of III
A.4.4 The Proof of IV
A.5 Fourier Transforms and Series
A.5.1 Fourier Transforms
A.5.2 Fourier Series
References and Author Index.
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登録日 2020.06.27
更新日 2020.06.28