Chapter 1．History of Magnetism 1
1.1．Physics and Metaphysics 3
1.2．Gilbert and Descartes 6
1.3．Rise of Modern Science 12
1.4．Electrodynamics 16
1.5．The Electron 23
1.6．The Demise of Classical Physics 26
1.7．Quantum Theory 31
1.8．Modern Foundations 35
1.9．Magnetic Bubbles 39
1.10．Ultimate Thin Films 44
1.11．Dilute Magnetic Alloys 47
1.12．New Directions 49
Chapter 2．Currents or Spins? 53
2.1．Charge Currents or Spins? 53
2.2．The Magnetic Dipole 56
2.3．The Magnetic Dipole-Dipole Interactions 57
2.4．The Exchange Interactions 63
2.5．Metals and Their Alloys 65
2.6．Superconductivity 68
2.7．The Need to Study Spin Angular Momentum 69
Chapter 3．Quantum Theory of Angular Momentum 70
3.1．Kinetic Angular Momentum 70
3.2．Spherical Harmonics 74
3.3．Reason for Integer l and m 78
3.4．Matrices of Angular Momentum 80
3.5．Pauli Spin Matrices 82
3.6．Compounding Angular Momentum 83
3.7．Equations of Motion of Interacting Angular Momenta 87
3.8．Coupled Boson Representation 87
3.9．Rotations 90
3.10．More on Compound Angular Momentum 92
3.11．Other Representations 95
3.12．Spins Ohe-Half:Special Tricks 96
3.13．Spins One 98
3.14．Quadratic Forms 100
3.15．Projection Operators 101
Chapter 4．Magnetism and the Many-Body Problem 104
4.1．Hamiltonian Physics and Degeneracy 104
4.2．The Pauli Principle 107
4.3．The Two-Fermion Problem 111
4.4．Electrons in One Dimension:A Theorem 113
4.5．The Wronskian 116
4.6．States of Three Electrons 118
4.7．Eigenfunctions of Total S2 and Sz 120
4.8．Hund's Rules 125
4.9．p3 Configuration 127
4.10．p2 and p4 Configurations 133
4.11．Second Quantization 139
4.12．Double Exchange 143
4.13．Superexchange 146
4.14．Jellium 149
4.15．Hubbard Model:An Introduction 154
4.16．Nagaoka's Ferromagnetism 163
4.17．One Dimension:Exact Solutions 167
4.18．Ferrimagnetism 168
4.19．Spin-Dependent Tunneling 172
Chapter 5．From Magnons to Solitons:Spin Dynamics 175
5.1．Spin Waves as Harmonic Oscillators 176
5.2．One-Magnon Eigenstates in Ferromagnets 185
5.3．Two-Magnon States and Eigenstates in Ferromagnets 186
5.4．Bound States in One Dimension 195
5.5．Bound States in Two and Three Dimensions 196
5.6．Antiferromagnetic Magnons:The One-Dimensional XY Model 200
5.7．Bethe's Solution of One-Dimensional Heisenberg Antiferromagnet 206
5.8．Linearized Antiferromagnetic Magnons 215
5.9．Ferrimagnetism 224
5.10．Some Rigorous Notions in Antiferro-and Ferri-Magnetism 226
5.11．Vortices 228
5.12．Solitons and Bloch Domain Walls:Introductory Material 231
5.13．Solitary Wave Solution 235
5.14．More on Magnetic Domains 241
5.15．Time-Dependent Phenomena 242
5.16．Majumdar-Ghosh Model and"Quantum Frustration" 247
5.17．Integer Spins 250
5.18．The AKLT Spin One Chain 254
5.19．Defective Antiferromagnets 255
Chapter 6．Magnetism in Metals 257
6.1．Bloch and Wannier States 259
6.2．Tight-Binding 260
6.3．Weak Magnetic Properties 267
6.4．Exchange in Solids:Construction of a Model Hamiltonian 273
6.5．Perturbation-Theoretic Derivation of Heisenberg Hamiltonian 281
6.6．Heisenberg Hamiltonian in Metals 284
6.7．Ordered Magnetic Metals:Deriving the Ground State 287
6.8．Kondo Effect 296
6.9．Spin Glasses 304
6.10．Magnetism without Localized Spins:Preliminaries 310
6.11．Degenerate Bands and Intra-Atomic Exchange Forces 314
6.12．Magnons in Metals 320
6.13．Marginal Magnetism of Impurities 327
6.14．Correlations and Equivalence to s-d Model 337
6.15．Periodic Anderson Model 342
Chapter 7．Statistical Thermodynamics 344
7.1．Spins in a Magnetic Field 344
7.2．The Partition Function 349
7.3．The Concept of the Molecular Field 354
7.4．Discontinuity in Specific Heat 358
7.5．Magnetic Susceptibility and Spontaneous Magnetization 361
7.6．Adiabatic Demagnetization 365
7.7．Antiferromagnetism 366
7.8．Short-Ranged versus Long-Ranged Interactions 369
7.9．Fermions,Bosons,and all that 375
Fermions 375
Bosons 375
Gaussian 376
Legendre Transformations 377
7.10．Gaussian and Spherical Models 378
Gaussian Model 379
Spherical Model 382
Watson's Integrals Generalized 387
7.11．Magnetic Susceptibility in Gaussian and Spherical Models 389
7.12．Spherical Antiferromagnet 392
7.13．Spherical Model Spin Glass 395
Magnetic Properties of Spin Glass 399
7.14．Thermodynamics of Magnons 407
7.15．Magnetism in Two Dimensions 414
7.16．The XY Model:1D 418
7.17．The XY Model:2D 426
7.18．Transfer Matrix of Plane Rotator Model 433
Chapter 8．The Ising Model 438
8.1．High Temperature Expansions 441
8.2．Graph Theory 445
8.3．Low Temperature Expansions and the Duality Relations 448
8.4．Peierls' Proof of Long Range Order 452
8.5．1D Ising Model in Longitudinal Fields 454
8.6．1D Ising Model in Transverse Fields 462
8.7．Concerning Quadratic Forms of Fermion Operators 474
8.8．Two-Dimensional Ising Model:The Transfer Matrix 478
8.9．Solution of Two-Dimensional Ising Model in Zero Field 485
8.10．Spontaneous Magnetization and Magnetic Susceptibility 494
8.11．Zeros of the Partition Function 502
8.12．Miscellania,Including 2D Antiferromagnets 507
8.13．The Three-Dimensional Ising Model 517
8.14．Ising Gauge Glass 526
8.15．Frustration 528
Chapter 9．Miscellaneous Advanced Topics 533
9.1．Critical Phenomena 533
9.2．Green Functions Formalism 536
9.3．Nonlinear Responses and Chaos 539
9.4．Kondo Phenomenon:The s-d Model Redux 539
9.5．Scaling,Renormalization and Information Theory 547
Bibliography 549
Index 561