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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

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Published: 1st May 2006
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This new version of a classic updates much of the material in earlier editions, including the first chapter, on the history of the field. Important modifications reflect major discoveries of the past decades. A historical perspective is maintained throughout. The reader is drawn into the process of discovery: starting with a phenomenon, finding plausible explanations and competing theories — and finally, the solution.The theory of magnetism is practically a metaphor for theoretical physics. The very first quantum many-body theory (Bethe's ansatz) was devised for magnetic chains, just as mean-field theory was invented a century ago by Weiss to explain Curie's Law.The first two chapters of this book are immensely readable, taking us from prehistory to the “spin valves” of the most recent past. Topics in subsequent chapters include: angular momenta and spin (Chapter 3), quantum theory of simple systems, followed by increasingly technical insights into ordered and random systems, thermal fluctuations, phase transitions, chaos and the like. Contemporary developments in nanotechnology now seek to take advantage of the electron's spin as well as of its charge. The time is not far off when nano-circuits made entirely of silicon exhibit such many-body properties as superconductivity or ferromagnetism — without any superconducting materials or magnetic ions being present. The reader of this book will be prepared for such exotic twenty-first century applications.Daniel C Mattis, BS, MS, PhD, Fellow of the American Physical Society (APS), is a frequent lecturer at research institutions and the author of several textbooks and numerous research articles. His expertise includes many-body theory, electrical conductivity, quantum theory of magnetism and most recently, nanotechnology. Prof. Mattis is on the editorial panel for high-temperature superconductivity of the International Journal of Modern Physics B and Modern Physics Letters B, both published by World Scientific. Currently serving as Professor in the Physics department at the University of Utah in Salt Lake City, Utah, USA, at various times he has been visiting Professor at Yale University (New Haven), State University of New York (Buffalo), Temple University (Philadelphia), and served as “Wei-Lun Visiting Professor” at the Chinese University of Hong Kong. A founding member of the “Few-Body Physics” section of the APS, he has also served as Chair of the standing committee of the APS for the “International Freedom of Scientists.”

.,." 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: 9789812386717
ISBN-10: 9812386718
Audience: General
Format: Paperback
Language: English
Number Of Pages: 565
Published: 1st May 2006
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 24.54 x 16.76  x 2.87
Weight (kg): 0.97