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| Prologue | |
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| History of Magnetism | |
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| Physics and Metaphysics | |
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| Gilbert and Descartes | |
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| Rise of Modern Science | |
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| Electrodynamics | |
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| The Electron | |
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| The Demise of Classical Physics | |
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| Quantum Theory | |
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| Modern Foundations | |
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| Magnetic Bubbles | |
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| Ultimate Thin Films | |
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| Dilute Magnetic Alloys | |
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| New Directions | |
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| Currents or Spins? | |
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| Charge Currents or Spins? | |
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| The Magnetic Dipole | |
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| The Magnetic Dipole-Dipole Interactions | |
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| The Exchange Interactions | |
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| Metals and Their Alloys | |
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| Superconductivity | |
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| The Need to Study Spin Angular Momentum | |
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| Quantum Theory of Angular Momentum | |
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| Kinetic Angular Momentum | |
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| Spherical Harmonics | |
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| Reason for Integer l and m | |
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| Matrices of Angular Momentum | |
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| Pauli Spin Matrices | |
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| Compounding Angular Momentum | |
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| Equations of Motion of Interacting Angular Momenta | |
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| Coupled Boson Representation | |
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| Rotations | |
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| More on Compound Angular Momentum | |
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| Other Representations | |
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| Spins One-Half: Special Tricks | |
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| Spins One | |
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| Quadratic Forms | |
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| Projection Operators | |
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| Magnetism and the Many-Body Problem | |
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| Hamiltonian Physics and Degeneracy | |
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| The Pauli Principle | |
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| The Two-Fermion Problem | |
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| Electrons in One Dimension: A Theorem | |
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| The Wronskian | |
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| States of Three Electrons | |
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| Eigenfunctions of Total S[superscript 2] and S[subscript z] | |
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| Hund's Rules | |
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| p[superscript 3] Configuration | |
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| p[superscript 2] and p[superscript 4] Configurations | |
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| Second Quantization | |
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| Double Exchange | |
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| Superexchange | |
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| Jellium | |
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| Hubbard Model: An Introduction | |
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| Nagaoka's Ferromagnetism | |
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| One Dimension: Exact Solutions | |
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| Ferrimagnetism | |
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| Spin-Dependent Tunneling | |
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| From Magnons to Solitons: Spin Dynamics | |
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| Spin Waves as Harmonic Oscillators | |
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| One-Magnon Eigenstates in Ferromagnets | |
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| Two-Magnon States and Eigenstates in Ferromagnets | |
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| Bound States in One Dimension | |
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| Bound States in Two and Three Dimensions | |
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| Antiferromagnetic Magnons: The One-Dimensional XY Model | |
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| Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet | |
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| Linearized Antiferromagnetic Magnons | |
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| Ferrimagnetism | |
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| Some Rigorous Notions in Antiferro- and Ferri-Magnetism | |
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| Vortices | |
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| Solitons and Bloch Domain Walls: Introductory Material | |
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| Solitary Wave Solution | |
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| More on Magnetic Domains | |
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| Time-Dependent Phenomena | |
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| Majumdar-Ghosh Model and "Quantum Frustration" | |
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| Integer Spins | |
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| The AKLT Spin One Chain | |
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| Defective Antiferromagnets | |
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| Magnetism in Metals | |
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| Bloch and Wannier States | |
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| Tight-Binding | |
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| Weak Magnetic Properties | |
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| Exchange in Solids: Construction of a Model Hamiltonian | |
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| Perturbation-Theoretic Derivation of Heisenberg Hamiltonian | |
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| Heisenberg Hamiltonian in Metals | |
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| Ordered Magnetic Metals: Deriving the Ground State | |
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| Kondo Effect | |
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| Spin Glasses | |
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| Magnetism without Localized Spins: Preliminaries | |
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| Degenerate Bands and Intra-Atomic Exchange Forces | |
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| Magnons in Metals | |
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| Marginal Magnetism of Impurities | |
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| Correlations and Equivalence to s-d Model | |
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| Periodic Anderson Model | |
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| Statistical Thermodynamics | |
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| Spins in a Magnetic Field | |
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| The Partition Function | |
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| The Concept of the Molecular Field | |
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| Discontinuity in Specific Heat | |
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| Magnetic Susceptibility and Spontaneous Magnetization | |
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| Adiabatic Demagnetization | |
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| Antiferromagnetism | |
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| Short-Ranged versus Long-Ranged Interactions | |
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| Fermions, Bosons, and all that | |
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| Fermions | |
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| Bosons | |
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| Gaussian | |
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| Legendre Transformations | |
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| Gaussian and Spherical Models | |
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| Gaussian Model | |
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| Spherical Model | |
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| Watson's Integrals Generalized | |
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| Magnetic Susceptibility in Gaussian and Spherical Models | |
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| Spherical Antiferromagnet | |
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| Spherical Model Spin Glass | |
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| Magnetic Properties of Spin Glass | |
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| Thermodynamics of Magnons | |
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| Magnetism in Two Dimensions | |
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| The XY Model: 1D | |
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| The XY Model: 2D | |
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| Transfer Matrix of Plane Rotator Model | |
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| The Ising Model | |
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| High Temperature Expansions | |
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| Graph Theory | |
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| Low Temperature Expansions and the Duality Relations | |
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| Peierls' Proof of Long Range Order | |
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| 1D Ising Model in Longitudinal Fields | |
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| 1D Ising Model in Transverse Fields | |
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| Concerning Quadratic Forms of Fermion Operators | |
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| Two-Dimensional Ising Model: The Transfer Matrix | |
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| Solution of Two-Dimensional Ising Model in Zero Field | |
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| Spontaneous Magnetization and Magnetic Susceptibility | |
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| Zeros of the Partition Function | |
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| Miscellania, Including 2D Antiferromagnets | |
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| The Three-Dimensional Ising Model | |
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| Ising Gauge Glass | |
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| Frustration | |
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| Miscellaneous Advanced Topics | |
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| Critical Phenomena | |
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| Green Functions Formalism | |
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| Nonlinear Responses and Chaos | |
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| Kondo Phenomenon: The s-d Model Redux | |
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| Scaling, Renormalization and Information Theory | |
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| Bibliography | |
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| Index | |