Principles of Condensed Matter Physics

P. M. Chaikin, T. C. Lubensky

Cambridge University Press, Sep 28, 2000 - Science - 699 pages

Now in paperback, this book provides an overview of the physics of condensed matter systems. Assuming a familiarity with the basics of quantum mechanics and statistical mechanics, the book establishes a general framework for describing condensed phases of matter based on symmetries and conservation laws. After surveying the structure and properties of materials with different symmetries, it explores the role of spatial dimensionality and microscopic interactions in determining the nature of phase transitions. Particular attention is given to critical phenomena and renormalization group methods. The properties of liquids, liquid crystals, quasicrystals, crystalline solids, magnetically ordered systems and amorphous solids are investigated in terms of their symmetry, generalized rigidity, hydrodynamics and topological defect structure. In addition to serving as a course text, this book is an essential reference for students and researchers in physics, applied physics, chemistry, materials science and engineering, who are interested in modern condensed matter physics.

Contents

• 1 Overview: 1
• 12 An example H₂O: 3
• 2 The liquidgas phase transition: 4
• 3 Spatial correlations in the liquid state: 5
• 4 Ice crystallized water: 8
• 5 Broken symmetry and rigidity: 10
• 6 Dislocations topological defects: 12
• 7 Universality of the water example: 13
• 8 Fluctuations and spatial dimension: 15
• 9 Overview of book: 16
• 13 Energies and potentials: 17
• 2 Van der Waals attraction: 18
• 3 Molecular hydrogen the HeitlerLondon approach: 20
• 4 Hardsphere repulsion: 22
• 5 Exchange interaction and magnetism: 24
• 6 The hydrogen molecule molecular orbitals and bands in metals: 25
• Bibliography: 28
• 2 Structure and scattering: 29
• 22 Photons neutrons or electrons: 33
• 23 The density operator and its correlation functions: 34
• 24 Liquids and gases: 38
• 1 Hardsphere liquids: 40
• 25 Crystalline solids: 43
• 2 The reciprocal lattice: 45
• 3 Periodic functions: 46
• 4 Bragg scattering: 47
• 26 Symmetry and crystal structure: 49
• 1 Twodimensional Bravais lattices: 50
• 2 Threedimensional Bravais lattices: 53
• 3 Close packed structures: 56
• 4 Space groups: 57
• 27 Liquid crystals: 58
• 2 SmecticsA and C: 61
• 3 Hexatic phases: 65
• 4 Discotic phases: 68
• 28 One and twodimensional order in threedimensional materials: 71
• 29 Incommensurate structures: 77
• 210 Quasicrystals: 82
• 211 Magnetic order: 85
• 212 Random isotropic fractals: 90
• Appendix 2A Fourier transforms: 97
• 2 d dimensions: 99
• 3 Transforms on a lattice: 100
• Bibliography: 101
• References: 102
• Problems: 103
• 3 Thermodynamics and statistical mechanics: 108
• 1 The first law of thermodynamics: 109
• 2 The second law of thermodynamics: 111
• 4 Thermodynamic potentials: 112
• 5 Stability criteria: 113
• 6 Homogeneous functions: 115
• 7 Equations of state: 116
• phase space and ensembles: 117
• 33 The ideal gas: 122
• 34 Spatial correlations in classical systems: 123
• 35 Ordered systems: 127
• 36 Symmetry order parameters and models: 132
• 1 Discrete symmetries: 135
• 2 Continuous symmetries: 137
• 3 Models: 139
• Appendix 3A Functional derivatives: 140
• Bibliography: 142
• 4 Meanfield theory: 144
• 41 BraggWilliams theory: 146
• 42 Landau theory: 151
• 43 The Ising and nvector models: 152
• 1 The nonlocal susceptibility and the correlation length: 154
• 2 On symmetry: 156
• 3 Some meanfield transitions: 157
• 44 The liquidgas transition: 159
• 1 The critical point and the critical isochore: 162
• 2 The coexistence curve: 165
• 45 The firstorder nematictoisotropic transition: 168
• 46 Multicritical points: 172
• 1 Tricritical points: 173
• 2 Metamagnets and FeCl₂: 175
• 3 He³ He⁴ mixtures and the BlumeEmeryGriffiths model: 179
• 4 Bicritical and tetracritical points: 181
• 5 Lifshitz points: 184
• 47 The liquidsolid transition: 188
• 1 Are all crystals BCC?: 189
• 2 Criterion for freezing: 192
• 4 Changes in density: 194
• 5 Density functional theory: 195
• 48 Variational meanfield theory: 198
• 2 The meanfield approximation: 200
• 3 The sstate Potts model: 201
• 4 The On classical Heisenberg model: 202
• 5 DebyeHuckel theory: 204
• Bibliography: 208
• References: 209
• 5 Field theories critical phenomena and the renormalization group: 213
• 51 Breakdown of meanfield theory: 214
• 1 Meanfield transitions revisited: 216
• 52 Construction of a field theory: 217
• 2 Lattice field theories and their continuum limit: 219
• 3 Gaussian integrals: 221
• 4 Meanfield theory from functional integrals: 223
• 5 Breakdown of meanfield theory revisited: 225
• 53 The selfconsistent field approximation: 226
• 1 The nvector model in the limit n oo: 229
• 54 Critical exponents universality and scaling: 230
• 2 Scaled equation of state: 234
• 3 Multicritical points: 235
• 4 Amplitude ratios: 236
• 5 Theoretical calculations of critical exponents and amplitude ratios: 237
• 56 The onedimensional Ising model: 242
• 2 Decimation and renormalization: 245
• 57 The MigdalKadanoff procedure: 248
• 2 General properties of recursion relations: 252
• 3 The Potts lattice gas and krypton on graphite: 253
• 58 Momentum shell renormalization group: 256
• 2 Correlation functions: 260
• 3 The Gaussian model: 261
• 4 The eexpansion: 263
• 5 nvector model with cubic anisotropy: 267
• 6 Quadratic anisotropy: 269
• 7 Crossover: 270
• 8 Dangerous irrelevant variables: 273
• 9 The utility of the eexpansion: 275
• Appendix 5A The HubbardStratonovich transformation: 276
• Appendix 5B Diagrammatic perturbation theory: 277
• Bibliography: 283
• 6 Generalized elasticity: 288
• 61 The xymodel: 289
• 2 Boundary conditions and external fields: 290
• 3 The Josephson scaling relation: 292
• 4 Fluctuations: 293
• 5 Longrange order quasilongrange order and disorder: 295
• 6 Resistance of a conducting medium: 297
• 62 On symmetry and nematic liquid crystals: 298
• 3 Cells with nonuniform n: 300
• 4 The Freedericksz transition: 302
• 5 The twisted nematic display: 304
• 6 Fluctuations and light scattering: 306
• Smectic liquid crystals: 308
• 1 The elastic free energy: 309
• 2 Fluctuations: 312
• 3 Nonlinearities: 314
• 4 The nematictosmecticA transition: 315
• strain and elastic energy: 316
• 2 The elastic free energy: 318
• 3 Isotropic and cubic solids: 319
• 4 Fluctuations: 321
• 5 Mercury chain salts onedimensional crystals: 322
• 6 Xenon on graphite a twodimensional crystal: 324
• 7 Vacancies and interstitials: 325
• 8 Bondangle order and rotational and translational elasticity: 328
• 9 Elastic constants from density functional theory: 329
• 65 Lagrangian elasticity: 330
• 2 Elasticity of classical harmonic lattices: 332
• the stress tensor: 334
• 2 Stressstrain relations: 337
• 3 The Eulerian stress tensor: 338
• 67 The nonlinear sigma model: 341
• Bibliography: 347
• correlation and response: 353
• 71 Dynamic correlation and response functions: 354
• 2 Response functions: 355
• 72 The harmonic oscillator: 359
• 2 The damped oscillator: 360
• 3 The response function: 362
• 4 Dissipation: 365
• 73 Elastic waves and phonons: 366
• 2 Acoustic phonons in a harmonic lattice: 367
• 74 Diffusion: 369
• 2 The Green function and dynamic response: 370
• 3 The response function: 371
• 4 External potentials and the Einstein relation: 373
• 5 Brownian motion: 375
• 6 Cooperative diffusion versus selfdiffusion: 376
• 7 Master equation for diffusion on a lattice: 378
• 75 Langevin theory: 381
• 2 Correlation functions for diffusion: 383
• 3 Shorttime behavior: 385
• 4 Fluctuationdissipation theorem for the harmonic oscillator: 387
• 5 The FokkerPlanck and Smoluchowski equations: 388
• 76 Formal properties of response functions: 390
• 2 Symmetry properties of response functions: 392
• 3 Dissipation: 394
• 4 Spectral representations of: 395
• 5 The fluctuationdissipation theorem: 397
• 6 Sum rules and moment expansions: 398
• 77 Inelastic scattering: 399
• 2 Fermi golden rule and neutron scattering: 400
• 3 The Fermi pseudopotential: 402
• 4 Coherent and incoherent scattering: 404
• 5 Crosssections and correlation functions: 405
• 6 Neutron scattering from crystals: 406
• 7 Magnetic scattering: 407
• 8 How neutron scattering experiments are actually done: 408
• 9 Scattering of charged particles and photons: 410
• Bibliography: 411
• Hydrodynamics: 417
• 82 A tutorial example rigid rotors on a lattice: 419
• 1 Description of the model: 420
• 2 The disordered phase: 421
• 3 The ordered phase: 426
• 4 Excitations from the classical ground state: 430
• 5 The Goldstone theorem: 432
• 7 Summary: 433
• 83 Spin systems: 434
• 2 Generalized Heisenberg models: 435
• 3 The planar magnet: 436
• 4 The isotropic antiferromagnet: 438
• 5 Isotropic ferromagnets: 439
• 84 Hydrodynamics of simple fluids: 440
• 1 Conservation laws: 441
• 2 Thermodynamics with mass motion: 443
• 3 The entropy production equation: 444
• 4 Dissipationless hydrodynamics: 445
• 5 Dissipation: 446
• 6 The NavierStokes equations: 448
• 7 Hydrodynamic modes: 449
• 8 Light scattering: 452
• 9 Twocomponent fluids: 453
• 85 Liquid crystals crystalline solids and superfluid helium: 454
• 2 SmecticA liquid crystals: 456
• 3 Crystalline solids: 459
• 4 Superfluid helium: 460
• 86 Stochastic models and dynamic critical phenomena: 464
• 2 Dissipative dynamics: 466
• 3 Dynamic scaling: 469
• 4 Poisson bracket terms: 472
• 5 Models with Poisson brackets: 475
• 6 Modemode coupling: 477
• 87 Nucleation and spinodal decomposition: 479
• 1 Nucleation with a nonconserved order parameter: 480
• 2 Symmetric unstable quench with model A dynamics: 483
• 3 Conserved order parameters and spinodal decomposition: 484
• Bibliography: 491
• Problems: 492
• 9 Topological defects: 495
• 1 Vortex pairs: 499
• 3 Order parameter spaces and homotopy: 501
• 92 Examples of topological defects: 506
• 2 Dislocations in smectic liquid crystals: 507
• 3 Periodic solids: 512
• 4 Volterra construction: 515
• 6 Disclinations in crystals: 517
• 7 Strength of crystals: 518
• 8 Crystal growth: 522
• 10 Nematic and hexatic liquid crystals: 524
• 93 Energies of vortices and dislocations: 526
• 2 Analogy with magnetism: 530
• 3 Energies of dislocations in crystals: 531
• 4 Dislocations in smectic liquid crystals: 536
• 94 Vortex unbinding and the KosterlitzThouless transition: 542
• 2 Vortex unbinding in two dimensions the Kosterlitz Thouless transition: 544
• 3 Superfluid helium films: 551
• 95 Dislocation mediated melting: 555
• 1 Effects of a substrate: 558
• 2 Experiments and numerical simulation: 559
• 96 The twistgrainboundary phase: 561
• 2 The thermodynamic critical field: 564
• 3 The lower critical field: 565
• 4 The upper critical field: 566
• 5 Xray scattering: 568
• 6 Analogy with superconductivity: 571
• Appendix 9A Notes on the KosterlitzThouless transition: 573
• 2 Longitudinal and transverse response: 575
• 3 The spin correlation function: 577
• Appendix 9B Duality and the Villain model: 578
• 1 Potts models: 579
• 2 The xy Villain and lattice Coulombgas models: 582
• Bibliography: 584
• Problems: 585
• Walls kinks and solitons: 590
• 101 Some simple examples: 591
• 102 Domain walls in meanfield theory: 595
• 1 The ϕ⁴ kink: 597
• 2 The sineGordon soliton: 599
• 103 The FrenkelKontorowa model: 601
• 2 Discommensurations: 602
• 3 Devils staircases and the FK phase diagram: 603
• 4 The continuum approximation: 605
• 5 Nature of solutions: 608
• 6 The minimum energy solution: 610
• 7 Repulsive interaction between discommensurations: 613
• 9 Compressional elastic constants: 614
• 10 Phasons: 615
• 11 Pinned phasons: 617
• 12 Extension to two dimensions: 618
• 104 Fluctuating walls: 620
• 2 Curvature: 623
• 3 Energy of a surface: 625
• 4 Fluctuations in the harmonic approximation: 626
• 5 Nonlinearities and renormalization in fluid membranes: 629
• 6 Polymerized membranes: 630
• 105 Arrays of fluctuating walls: 635
• 2 Honeycomb lattice of walls: 638
• 4 Dislocations and the CI transition: 640
• 106 Roughening and faceting: 643
• 2 The roughening transition: 646
• 3 Faceting: 648
• Bibliography: 655
• References: 656
• Glossary: 662
• Index: 685

Bibliographic information

• Title: Principles of Condensed Matter Physics
• Authors: P. M. Chaikin, T. C. Lubensky
• Edition: illustrated, reprint, revised
• Publisher: Cambridge University Press, 2000
• ISBN: 0521794501, 9780521794503
• Length: 699 pages
• Subjects: Science / Chemistry / Physical & Theoretical; Science / Physics / Condensed Matter; Science / Physics / General; Technology & Engineering / Electronics / General; Technology & Engineering / Materials Science / General