The Theory of Magnetism II: Thermodynamics and Statistical Mechanics

ISBN-13: 9783642824074 / Angielski / Miękka / 2011 / 184 str.

Daniel C. Mattis

Opis

What is thermodynamics? What does statistical physics teach us? In the pages of this slim book, we confront the answers. The reader will discover that where thermodynami cs provi des a 1 arge scal e, macroscopi c theory of the ef fects of temperature on physical systems, statistical mechanics provides the microscopic analysis of these effects which, invariably, are the results of thermal disorder. A number of systems in nature undergo dramatic changes in aspect and in their properties when subjected to changes in ambient temperature or pres sure, or when electric or magnetic fields are applied. The ancients already knew that a liquid, a solid, or a gas can represent different states of the same matter. But what is meant by "state"? It is here that the systematic study of magnetic materials has provided one of the best ways of examining this question, which is one of the principal concerns of statistical physics (alias "statistical mechanics") and of modern thermodynamics."

Spis treści

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).