Springer Solid-State Sciences

1. Introduction and Guide to This Text.- 2. Statistical Thermodynamics.- 2.1 Spins in a Magnetic Field.- 2.2 The Partition Function.- 2.3 The Concept of the Molecular Field.- 2.4 Discontinuity in Specific Heat.- 2.5 Magnetic Susceptibility and Spontaneous Magnetization.- 2.6 Antiferromagnetism.- 2.7 Short-Ranged Versus Long-Ranged Interactions.- 2.8 Fermions, Bosons, and All That.- 2.8.1 Fermions.- 2.8.2 Bosons.- 2.8.3 Gaussian.- 2.8.4 Legendre Transformations.- 2.9 Gaussian and Spherical Models.- 2.9.1 Gaussian Model.- 2.9.2 Spherical Model.- 2.9.3 Watson's Integrals Generalized.- 2.10 Magnetic Susceptibility in Gaussian and Spherical Models.- 2.11 Spherical Antiferromagnet.- 2.12 Spherical Model Spin Glass.- 2.13 Magnetic Properties of Spin Glass.- 2.14 Thermodynamics of Magnons.- 2.15 Magnetism in Two Dimensions.- 2.16 The XY Mode1:1D.- 2.17 The XY Model:2D.- 2.18 Transfer Matrix of Plane Rotator Model.- 3. The Ising Model.- 3.1 High Temperature Expansions.- 3.2 Graph Theory.- 3.3 Low Temperature Expansions and the Duality Relations.- 3.4 Peierls' Proof of Long Range Order.- 3.5 1D Ising Model in Longitudinal Fields.- 3.6 1D Ising Model in Transverse Fields.- 3.7 Concerning Quadratic Forms of Fermion Operators.- 3.8 Two-Dimensional Ising Model: The Transfer Matrix.- 3.9 Solution of Two-Dimensional Ising Model in Zero Field.- 3.10 Spontaneous Magnetization and Magnetic Susceptibility.- 3.11 Zeros of the Partition Function.- 3.12 Miscellania, Including 2D Antiferromagnets.- 3.13 The Three-Dimensional Ising Model.- References.- List of Tables.- Errata for The Theory of Magnetism I (Springer Series in Solid-State Sciences, Vol. 17).