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Theory Of Magnetism Made Simple, The : An Introduction To Physical Concepts And To Some Useful Mathematical Methods - Daniel C. Mattis

Theory Of Magnetism Made Simple, The

An Introduction To Physical Concepts And To Some Useful Mathematical Methods


Published: 1st May 2006
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The original edition of "The Theory of Magnetism" developed the various relevant topics using modern methods adapted for the many-body problem and thus it became popular (reportedly the "most-stolen" book from the exhibition stalls at the March meeting of the American Physical Society!). It presented and taught the fermionic field theory central to Onsager's analysis of the statistical mechanics of the two-dimensional Ising model of magnetism. In its pages the Lieb-Mattis theorems on magnetic ordering of electronic energy levels and on the absence of ferromagnetism in one dimension were restated and proved in a form accessible to students. The exchange mechanism in insulators and the Ruderman-Kittel interaction in metals were some of the innovative topics presented to the reader. Spin waves and their interactions were analyzed in some detail. The first chapter, on the history of physics as seen through the prism of research in magnetism, co-authored with Dr Noemi Mattis, proved especially popular. In this new edition, while retaining much of the material in earlier editions, especially the first chapter, the author has eliminated some of the bulk (the most recent edition was in two volumes) and added a number of new subjects. Among these are the effects of lowering the dimensionality (exact solutions of some important models in zero and one dimension are exhibited and contrasted with the three-dimensional versions) and the importance of the two-body Coulomb interactions. The reader is introduced to the topic of critical exponents. Quoting a novel theorem by Lieb and exotic band structures, the author re-examines the origins of ferromagnetism. In the presentation, physical principles come first, the mathematics second. Developing the reader's intuition and mastery of the subject takes precedence.

.,." an excellent resource for anyone working in magnetism or theoretical condensed matter physics ..."

Prologuep. v
History of Magnetismp. 1
Physics and Metaphysicsp. 3
Gilbert and Descartesp. 6
Rise of Modern Sciencep. 12
Electrodynamicsp. 16
The Electronp. 23
The Demise of Classical Physicsp. 26
Quantum Theoryp. 31
Modern Foundationsp. 35
Magnetic Bubblesp. 39
Ultimate Thin Filmsp. 44
Dilute Magnetic Alloysp. 47
New Directionsp. 49
Currents or Spins?p. 53
Charge Currents or Spins?p. 53
The Magnetic Dipolep. 56
The Magnetic Dipole-Dipole Interactionsp. 57
The Exchange Interactionsp. 63
Metals and Their Alloysp. 65
Superconductivityp. 68
The Need to Study Spin Angular Momentump. 69
Quantum Theory of Angular Momentump. 70
Kinetic Angular Momentump. 70
Spherical Harmonicsp. 74
Reason for Integer l and mp. 78
Matrices of Angular Momentump. 80
Pauli Spin Matricesp. 82
Compounding Angular Momentump. 83
Equations of Motion of Interacting Angular Momentap. 87
Coupled Boson Representationp. 87
Rotationsp. 90
More on Compound Angular Momentump. 92
Other Representationsp. 95
Spins One-Half: Special Tricksp. 96
Spins Onep. 98
Quadratic Formsp. 100
Projection Operatorsp. 101
Magnetism and the Many-Body Problemp. 104
Hamiltonian Physics and Degeneracyp. 104
The Pauli Principlep. 107
The Two-Fermion Problemp. 111
Electrons in One Dimension: A Theoremp. 113
The Wronskianp. 116
States of Three Electronsp. 118
Eigenfunctions of Total S[superscript 2] and S[subscript z]p. 120
Hund's Rulesp. 125
p[superscript 3] Configurationp. 127
p[superscript 2] and p[superscript 4] Configurationsp. 133
Second Quantizationp. 139
Double Exchangep. 143
Superexchangep. 146
Jelliump. 149
Hubbard Model: An Introductionp. 154
Nagaoka's Ferromagnetismp. 163
One Dimension: Exact Solutionsp. 167
Ferrimagnetismp. 168
Spin-Dependent Tunnelingp. 172
From Magnons to Solitons: Spin Dynamicsp. 175
Spin Waves as Harmonic Oscillatorsp. 176
One-Magnon Eigenstates in Ferromagnetsp. 185
Two-Magnon States and Eigenstates in Ferromagnetsp. 186
Bound States in One Dimensionp. 195
Bound States in Two and Three Dimensionsp. 196
Antiferromagnetic Magnons: The One-Dimensional XY Modelp. 200
Bethe's Solution of One-Dimensional Heisenberg Antiferromagnetp. 206
Linearized Antiferromagnetic Magnonsp. 215
Ferrimagnetismp. 224
Some Rigorous Notions in Antiferro- and Ferri-Magnetismp. 226
Vorticesp. 228
Solitons and Bloch Domain Walls: Introductory Materialp. 231
Solitary Wave Solutionp. 235
More on Magnetic Domainsp. 241
Time-Dependent Phenomenap. 242
Majumdar-Ghosh Model and "Quantum Frustration"p. 247
Integer Spinsp. 250
The AKLT Spin One Chainp. 254
Defective Antiferromagnetsp. 255
Magnetism in Metalsp. 257
Bloch and Wannier Statesp. 259
Tight-Bindingp. 260
Weak Magnetic Propertiesp. 267
Exchange in Solids: Construction of a Model Hamiltonianp. 273
Perturbation-Theoretic Derivation of Heisenberg Hamiltonianp. 281
Heisenberg Hamiltonian in Metalsp. 284
Ordered Magnetic Metals: Deriving the Ground Statep. 287
Kondo Effectp. 296
Spin Glassesp. 304
Magnetism without Localized Spins: Preliminariesp. 310
Degenerate Bands and Intra-Atomic Exchange Forcesp. 314
Magnons in Metalsp. 320
Marginal Magnetism of Impuritiesp. 327
Correlations and Equivalence to s-d Modelp. 337
Periodic Anderson Modelp. 342
Statistical Thermodynamicsp. 344
Spins in a Magnetic Fieldp. 344
The Partition Functionp. 349
The Concept of the Molecular Fieldp. 354
Discontinuity in Specific Heatp. 358
Magnetic Susceptibility and Spontaneous Magnetizationp. 361
Adiabatic Demagnetizationp. 365
Antiferromagnetismp. 366
Short-Ranged versus Long-Ranged Interactionsp. 369
Fermions, Bosons, and all thatp. 375
Fermionsp. 375
Bosonsp. 375
Gaussianp. 376
Legendre Transformationsp. 377
Gaussian and Spherical Modelsp. 378
Gaussian Modelp. 379
Spherical Modelp. 382
Watson's Integrals Generalizedp. 387
Magnetic Susceptibility in Gaussian and Spherical Modelsp. 389
Spherical Antiferromagnetp. 392
Spherical Model Spin Glassp. 395
Magnetic Properties of Spin Glassp. 399
Thermodynamics of Magnonsp. 407
Magnetism in Two Dimensionsp. 414
The XY Model: 1Dp. 418
The XY Model: 2Dp. 426
Transfer Matrix of Plane Rotator Modelp. 433
The Ising Modelp. 438
High Temperature Expansionsp. 441
Graph Theoryp. 445
Low Temperature Expansions and the Duality Relationsp. 448
Peierls' Proof of Long Range Orderp. 452
1D Ising Model in Longitudinal Fieldsp. 454
1D Ising Model in Transverse Fieldsp. 462
Concerning Quadratic Forms of Fermion Operatorsp. 474
Two-Dimensional Ising Model: The Transfer Matrixp. 478
Solution of Two-Dimensional Ising Model in Zero Fieldp. 485
Spontaneous Magnetization and Magnetic Susceptibilityp. 494
Zeros of the Partition Functionp. 502
Miscellania, Including 2D Antiferromagnetsp. 507
The Three-Dimensional Ising Modelp. 517
Ising Gauge Glassp. 526
Frustrationp. 528
Miscellaneous Advanced Topicsp. 533
Critical Phenomenap. 533
Green Functions Formalismp. 536
Nonlinear Responses and Chaosp. 539
Kondo Phenomenon: The s-d Model Reduxp. 539
Scaling, Renormalization and Information Theoryp. 547
Bibliographyp. 549
Indexp. 561
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9789812385796
ISBN-10: 9812385797
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 580
Published: 1st May 2006
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 24.94 x 17.22  x 3.28
Weight (kg): 1.12