Verfügbarkeit: Principles of condensed matter physics

Principles of condensed matter physics:

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Bibliographische Detailangaben
Hauptverfasser:	Chaikin, Paul M. (VerfasserIn), Lubensky, Tom C. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2010
Ausgabe:	5. printing
Schlagworte:	Kondensierte Materie Festkörperphysik
Online-Zugang:	Inhaltsverzeichnis Inhaltsverzeichnis
Beschreibung:	Includes bibliographical references and index
Beschreibung:	XX, 699 S. Ill., graph. Darst.
ISBN:	9780521794503

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface xvii 1 Overview 1 1.1 Condensed matter physics 1 1.2 An example - H2O 3 1 Gaseous and liquid states 3 2 The liquid-gas 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 1 Energy scales 17 2 Van der Waals attraction 18 3 Molecular hydrogen - the Heitler-London approach 20 4 Hard-sphere repulsion 22 5 Exchange interaction and magnetism 24 6 The hydrogen molecule, molecular orbitais, and bands in metals 25 Bibliography 28 References 28 2 Structure and scattering 29 2.1 Elementary scattering theory - Bragg s law 29 2.2 Photons, neutrons, or electrons 33 23 The density operator and its correlation functions 34 2.4 Liquids and gases 38 1 Hard-sphere liquids 40 2.5 Crystalline solids 43 1 Unit cells and the direct lattice 43 2 The reciprocal lattice 45 vu viii Contents 3 Periodic functions 46 4 Bragg scattering 47 Í.6 Symmetry and crystal structure 49 1 Two-dimensional Bravais lattices 50 2 Three-dimensional Bravais lattices 53 3 Close packed structures 56 4 Space groups 57 2.7 Liquid crystals 58 1 Isotropie, nematic and cholesteric phases 58 2 Smectics-A and -C 61 3 Hexatic phases 65 4 Discotic phases 68 5 Lyotropic liquid crystals and microemulsions 68 2.8 One- and two-dimensional order in three-dimensional materials 71 2.9 Incommensurate structures 77 2.10 Quasicrystals 82 2.11 Magnetic order 85 2.12 Random isotropie fractals 90 Appendix 2A Fourier transforms 97 1 One dimension 97 2 d dimensions 99 3 Transforms on a lattice 100 Bibliography 101 References 102 Problems 103 3 Thermodynamics and statistical mechanics 108 3.1 Thermodynamics of homogeneous fluids 108 1 The first law of thermodynamics 109 2 The second law of thermodynamics 111 3 The third law of thermodynamics 111 4 Thermodynamic potentials 112 5 Stability criteria 113 6 Homogeneous functions 115 7 Equations of state 116 3.2 Statistical mechanics: phase space and ensembles 117 33 The ideal gas 122 3.4 Spatial correlations in classical systems 123 3.5 Ordered systems 127 3.6 Symmetry, order parameters, and models 132 1 Discrete symmetries 135 2 Continuous symmetries 137 Contents ix 3 Models 139 Appendix ЗА Functional derivatives 140 Bibliography 142 References 142 Problems 142 4 Mean-field theory 144 4.1 Bragg-Williams theory 146 4.2 Landau theory 151 4.3 The Ising and η -vector models 152 1 The nonlocal susceptibility and the correlation length 154 2 On symmetry 156 3 Some mean-field transitions 157 4.4 The liquid-gas transition 159 1 The critical point and the critical isochore 162 2 The coexistence curve 165 4.5 The first-order nematic-to-isotropic transition 168 4.6 Multicritical points 172 1 Tricritical points 173 2 Metamagnets and FeCh 175 3 He3 — He4 mixtures and the Blume-Emery-Griffiths model 179 4 Bicritical and tetracritical points 181 5 Lifshitz points 184 4.7 The liquid-solid transition 188 1 Are all crystals BCC? 189 2 Criterion for freezing 192 3 Improvements of the theory 192 4 Changes in density 194 5 Density functional theory 195 4.8 Variational mean-field theory 198 1 Two inequalities 198 2 The mean-field approximation 200 3 The s-state Potts model 201 4 The On classical Heisenberg model 202 5 Debye-Hiickel theory 204 Bibliography 208 References 209 Problems 209 5 Field theories, critical phenomena, and the renormalization group 213 5.1 Breakdown of mean-field theory 214 Contents 1 Mean-field transitions revisited 216 5.2 Construction of a field theory 217 1 Coarse graining 217 2 Lattice field theories and their continuum limit 219 3 Gaussian integrals 221 4 Mean-field theory from functional integrals 223 5 Breakdown of mean-field theory revisited 225 53 The self-consistent field approximation 226 1 The n-vector model in the limit η -* oo 229 5.4 Critical exponents, universality, and scaling 230 1 Exponents and scaling relations 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 5.5 The Kadanoff construction 237 5.6 The one-dimensional Ising model 242 1 Exact solution 242 2 Decimation and renormalization 245 5.7 The Migdal-Kadanoff procedure 248 1 The Ising model on a hypercubic lattice 248 2 General properties of recursion relations 252 3 The Potts lattice gas and krypton on graphite 253 5.8 Momentum shell renormalization group 256 1 Thinning of degrees of freedom and rescaling 256 2 Correlation functions 260 3 The Gaussian model 261 4 The 6-expansion 263 5 η -vector model with cubic anisotropy 267 6 Quadratic anisotropy 269 7 Crossover 270 8 Dangerous irrelevant variables 273 9 The utility of the e-expansion 275 Appendix 5A The Hubbard-Stratonovich transformation 276 Appendix 5B Diagrammatic perturbation theory 277 Bibliography 283 References 283 Problems 283 6 Generalized elasticity 288 6.1 The xy-model 289 1 The elastic free energy 289 Contents xi 2 Boundary conditions and external fields 290 3 The Josephson scaling relation 292 4 Fluctuations 293 5 Long-range order, quasi-long-range order, and disorder 295 6 Resistance of a conducting medium 297 6.2 On symmetry and nematic liquid crystals 298 1 n-vector elastic energy 298 2 The Frank free energy of nematic liquid crystals 298 3 Cells with non-uniform η 300 4 The Freedericksz transition 302 5 The twisted nematic display 304 6 Fluctuations and light scattering 306 6.3 Smectic liquid crystals 308 1 The elastic free energy 309 2 Fluctuations 312 3 Nonlinearities 314 4 The nematic-to-smectic-/! transition 315 6.4 Elasticity of solids: strain and elastic energy 316 1 The strain tensor 316 2 The elastic free energy 318 3 Isotropie and cubic solids 319 4 Fluctuations 321 5 Mercury chain salts - one-dimensional crystals 322 6 Xenon on graphite - a two-dimensional crystal 324 7 Vacancies and interstitials 325 8 Bond-angle order and rotational and translational elasticity 328 9 Elastic constants from density functional theory 329 6.5 Lagrangian elasticity 330 1 Classical theory of elasticity 330 2 Elasticity of classical harmonic lattices 332 6.6 Elasticity of solids: the stress tensor 334 1 The Lagrangian stress tensor 334 2 Stress-strain relations 337 3 The Eulerian stress tensor 338 6.7 The nonlinear sigma model 341 Bibliography 347 References 347 Problems 347 7 Dynamics: correlation and response 353 7.1 Dynamic correlation and response functions 354 1 Correlation functions 354 xii Contents 2 Response functions 355 7.2 The harmonic oscillator 359 1 The undamped oscillator 359 2 The damped oscillator 360 3 The response function 362 4 Dissipation 365 73 Elastic waves and phonons 366 1 Sound waves in an elastic continuum 366 2 Acoustic phonons in a harmonic lattice 367 7.4 Diffusion 369 1 Fick slaw 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 self-diffusion 376 7 Master equation for diffusion on a lattice 378 7.5 Langevin theory 381 1 Random forces and thermal equilibrium 381 2 Correlation functions for diffusion 383 3 Short-time behavior 385 4 Fluctuation-dissipation theorem for the harmonic oscillator 387 5 The Fokker-Planck and Smoluchowski equations 388 7.6 Formal properties of response functions 390 1 Response to external fields 390 2 Symmetry properties of response functions 392 3 Dissipation 394 4 Spectral representations of χ^(φ 395 5 The fluctuation-dissipation theorem 397 6 Sum rales and moment expansions 398 7.7 Inelastic scattering 399 1 Scattering geometry and partial cross-sections 399 2 Fermi golden rule and neutron scattering 400 3 The Fermi pseudopotential 402 4 Coherent and incoherent scattering 404 5 Cross-sections 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 References 411 Contents xiii Problems 411 8 Hydrodynamics 417 8.1 Conserved and broken-symmetry variables 417 8.2 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 6 Kubo formulae 432 7 Summary 433 8.3 Spin systems 434 1 Spin dynamics 434 2 Generalized Heisenberg models 435 3 The planar magnet 436 4 The isotropie antiferromagnet 438 5 Isotropie ferromagnets 439 8.4 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 Navier-Stokes equations 448 7 Hydrodynamic modes 449 8 Light scattering 452 9 Two-component fluids 453 8.5 Liquid crystals, crystalline solids, and superfluul helium 454 1 Nematic liquid crystals 454 2 Smectic-^ liquid crystals 456 3 Crystalline solids 459 4 Superfluid helium 460 8.6 Stochastic models and dynamic critical phenomena 464 1 Critical slowing down and the conventional theory 464 2 Dissipative dynamics 466 3 Dynamic scaling 469 4 Poisson bracket terms 472 5 Models with Poisson brackets 475 6 Mode-mode coupling 477 8.7 Nucleation and spinodal decomposition 479 1 Nucleation with a nonconserved order parameter 480 2 Symmetric unstable quench with model A dynamics 483 xiv Contents 3 Conserved order parameters and spinodal decomposition 484 Bibliography 491 References 491 Problems 492 9 Topological defects 495 9.1 Characterization of topological defects 495 1 Vortex pairs 499 2 Order parameters with more than two components 499 3 Order parameter spaces and homotopy 501 9.2 Examples of topological defects 506 1 Vortices in xy-models 506 2 Dislocations in smectic liquid crystals 507 3 Periodic solids 512 4 Volterra construction 515 5 Hexagonal and close-packed lattices 515 6 Disclinations in crystals 517 7 Strength of crystals 518 8 Crystal growth 522 9 Grain boundaries 522 10 Nematic and hexatic liquid crystals 524 93 Energies of vortices and dislocations 526 1 Simple calculation of xy-vortex energies 526 2 Analogy with magnetism 530 3 Energies of dislocations in crystals 531 4 Dislocations in smectic liquid crystals 536 9.4 Vortex unbinding and the Kosterlitz-Tbouless transition 542 1 Vortices and the spin-wave stiffness 542 2 Vortex unbinding in two dimensions - the Kosterlitz- Thouless transition 544 3 Superfluid helium films 551 9.5 Dislocation mediated melting 555 1 Effects of a substrate 558 2 Experiments and numerical simulation 559 9.6 The twist-grain-boandary phase 561 1 Structure of the TGB phase 561 2 The thermodynamic critical field 564 3 The lower critical field 565 4 The upper critical field 566 5 X-ray scattering 568 6 Analogy with superconductivity 571 Appendix 9A Notes on the Kosterlitz-Thouless transition 573 Contents xv 1 Integration of the KT recursion relations 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 Coulomb-gas models 582 Bibliography 584 References 584 Problems 585 10 Walls, kinks and solitons 590 10.1 Some simple examples 591 10.2 Domain walls in mean-field theory 595 1 The φ4 kink 597 2 The sine-Gordon soliton 599 3 Dynamics 599 10.3 The Frenkel-Kontorowa model 601 1 Introduction 601 2 Discommensurations 602 3 Devil s 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 8 X-ray diffraction 613 9 Compressional elastic constants 614 lOPhasons 615 11 Pinned phasons 617 12 Extension to two dimensions 618 10.4 Fluctuating walls 620 1 Differential geometry and the total surface area 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 630 103 Arrays of fluctuating walls 635 1 Fluctuating walls and steric entropy 635 2 Honeycomb lattice of walls 638 3 Elasticity of sterically stabilized phases 638 4 Dislocations and the CI transition 640 10.6 Roughening and faceting 643 1 The solid-on-solid and discrete Gaussian models 643 xvi Contents 2 The roughening transition 646 3 Faceting 648 Bibliography 655 References 656 Problems 656 Glossary 662 Index 685
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title	Principles of condensed matter physics
title_auth	Principles of condensed matter physics
title_exact_search	Principles of condensed matter physics
title_full	Principles of condensed matter physics P. M. Chaikin ; T. C. Lubensky
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title_short	Principles of condensed matter physics
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topic_facet	Kondensierte Materie Festkörperphysik
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