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Kardar M. — Statistical physics of fields
Kardar M. — Statistical physics of fields

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Название: Statistical physics of fields

Автор: Kardar M.

Аннотация:

While many scientists are familiar with fractals, fewer are familiar with scale-invariance and universality which underly the ubiquity of their shapes. These properties may emerge from the collective behaviour of simple fundamental constituents, and are studied using statistical field theories. Initial chapters connect the particulate perspective developed in the companion volume, to the coarse grained statistical fields studied here. Based on lectures taught by Professor Kardar at MIT, this textbook demonstrates how such theories are formulated and studied. Perturbation theory, exact solutions, renormalization groups, and other tools are employed to demonstrate the emergence of scale invariance and universality, and the non-equilibrium dynamics of interfaces and directed paths in random media are discussed. Ideal for advanced graduate courses in statistical physics, it contains an integrated set of problems, with solutions to selected problems at the end of the book and a complete set available to lecturers at www.cambridge.org/9780521873413.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2007

Количество страниц: 372

Добавлена в каталог: 08.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\epsilon$-expansion      87
Amplitude ratio      28 39 147
Analyticity      22
Anderson localization      241
Anisotropy      96 216 336 342
Anisotropy, Ising model      337
Anisotropy, random walk      336
Anomalous dimension      65
asymptotic freedom      133
Asymptotic series      93
Basin of attraction      65
Berker      114 174
Bethe ansatz      225
Bicritical      343
Binary alloy      14 260
Blume — Emery — Griffith      100
Bond moving      112
Borel summation      93
Bragg peak      176
Branched lattice animal      150 332
Brillouin zone      4 66
Broad probability distribution      210
Brownian motion      188
Burgers’ equation      206
Burger’s circuit      178
Burger’s vector      178
Capillary length      198
Capillary wave      49 283
Cayley tree      155
Central limit theorem      2 22 213
Characteristic function      212
Clock model      119 152 186
Coarse grain      6 20 60 80 217
coexistence      10
Cole — Hopf      205 229 231
Coleman — Weinberg mechanism      313
Collective modes      2
confinement      133
Connected average      75
Connected correlation function      13
Connected diagram      77
Conservation law      199 200
continuum limit      220
Contraction      74 76
Convexity      14 261
Correlation function      37 59 75 102 196 217
correlation length      13 47 57 58 103
Coulomb gas      168
Coulomb potential      40
Critical behavior      148
Critical exponent $\alpha$      12 28 89 147 162 314
Critical exponent $\beta$      11 27 89 148 314
Critical exponent $\Delta$      314
Critical exponent $\eta$      37 39 107 138 148 162 176 314
Critical exponent $\gamma$      12 28 89 148 314
Critical exponent $\nu$      14 39 62 89 138 139 148 162 314
Critical exponents      11 42 314
Critical opalescence      10 13
Critical point      10 54
Critical slowing down      193
Crystal anisotropy      94 303
Cubic anisotropy      95 306 309
Cubic invariant      32 268
Cumulant      75 77 84 212
Curie temperature      10
Debye — Waller factor      177
Decimation      104 112
Detailed balance      116
Diagrammatic representation      76 309
Diffusion      189
Dilation symmetry      59
Directed path      209 216 217
Directed polymer in random medium      229
Disclination      180
Discontinuous transition      32 268
Dislocation      178
Domain wall      31 237
Driven diffusion      201 207
Duality      128 184 354
Duality, energy      152
Duality, magnetic field      150 333
Duality, percolation      155
Duality, Potts model      334
Dynamic exponent      193
Dynamic programming      240
Dynamic scaling      199 204
Effective Hamiltonian      21
Einstein relation      190 195 202
Elastic moduli      8
Elasticity      3
Elitzur’s theorem      131
Equilibration time      117
Equivalent neighbor      15 262
Essential singularity      174
Exponent identities      57
Exponential decay of correlations      164
External points      76
Ferromagnet      10
Feynman path      209
First order transition      32 268
Fisher exponent identity      59 314
Fixed line      171
Fixed point      64 90 106 111
Fixed point, Gaussian      91
Fixed point, O(n)      91
Flow equation      83
Fluctuation induced discontinuous transition      313
Fluctuation-dissipation condition      191 194 201
Fokker — Planck equation      191 194 207
Forward scattering      244
Fourier mode      3 37 66 73
Fractal      59 139 196
Frank constant      180
Frobenius’ theorem      103 116 148
Frustration      233
Functional integral      24 44
Galilean invariance      207
Gap exponent      55
Gauge symmetry      49 131 133 154 285
Gaussian Integrals      43
Gaussian model      66 68 73 133 138
GENERIC      27 196 200
Generic scale invariance      196 199
Ginzburg criterion      47
Goldstone mode      29 36 39 96 156 175 313
Grand partition function      15 265
Halperin      177 179
heat capacity      28 47
Heisenberg model      99 103
Hexagonal lattice      121
Hexatic      180
Hierarchical lattice      114
Higgs mechanism      286
High temperature expansion      125
Homogeneity      54 296
Homogeneous function      55 58 62 292
Hyperscaling relation      59 62 71 296 314
Hysteresis      14 262
Independent path approximation      234
Internal point      76
Irrelevant      65
Ising model      14 262
Ising model, one dimension      101 127
Ising model, square lattice      140
Ising model, two dimensions      128
Isotropic      7 22 175
Josephson exponent identity      58
Kadanoff scaling      60 92
Kosterlitz      171 177
Kosterlitz — Thouless      165 174
KPZ equation      204
Lame coefficient      8 175
Landau — Ginzburg      21 23 30 49 73 192 285
Langevin equation      188 197
Latent heat      71 294
Lattice      3 98
Lattice animal      322
Lattice gas      15 265
Lattice gauge theory      131
Lindemann criterion      176 187
Line tension      221
Liquid crystal      181
Liquid-gas      21
Liquid-gas condensation      9
Locality      6 21
Localization length      242
Locator expansion      244
Log-normal distribution      210 214
Long-range interaction      52 97 185
Long-range order      29 41 139
Longitudinal      8 36 175
Longitudinal susceptibility      28 39 93 298
Loop model      149 185 324 356
Lorentzian      37
low-temperature expansion      123
Lower critical dimension      42 52
Magnet      10
magnetization      10 63
Majority rule      104 108
Marginal      65
Markov process      115 135 140 217
Matrix model      182 344
Mean-field theory      24
Melting      176 177 187
Mermin — Wagner theorem      42 158
Mesoscopic      20 22
Metastability      14 262
Metastable      26
Metropolis      116 122
Migdal — Kadanoff      112 118 155 320
Mixing entropy      14 260
Monte Carlo simulation      100 114
Mott      242
Mueller — Hartmann and Zittartz      340
Navier — Stokes      2 206
Nelson      177 179
Niemeijer — Van Leeuwen      108 117 317
Noether’s theorem      200 205
Non-renormalization condition      203 207
Nonlinear $\sigma$ model      156 181 185 343
Normal mode      3 30
O(n) model      99
Onsager      148
Optimal path      238
Order parameter      11 20 29 176
Orientational order      177
Orthogonal matrix      247 344
Paramagnet      10
Partition function      19
path integral      220 229
Percolation      150 154 322 332
Permutation symmetry      99 119
Perturbation theory      74
Phantom polymer      134
phase diagram      9
Phase transition      9 148
Phenomenological parameter      23
Phonon      3 175
Polyakov      158
Position space RG      104
Potts model      118 320 322 328 330
Power law decay of correlations      164
Propagator      76 77
Quantum electrodynamics      132
Quantum interference      241
Quasi-long range order      164 176
Quench average      211
Quenched disorder      209 211
Random bond      237
Random cluster expansion      150 331
Random field      51
random matrix      242 247
Random walk      135 139
Reciprocal lattice      176
Recursion relation      64 83 106 110 171
Reduced temperature      11 47
Relaxation time      190 193 199
Relevant      65
Renormalization group      60 68
Renormalize      82
Replica method      210 213 230
Rescale      82
Response function      12
Restricted solid on solid model      184 355
Rotation      7 22
roughening      183 184 186 350 354
Roughness exponent      198
Rushbrooke exponent identity      57 314
Saddle point      15 24 45 264
Scale invariance      59 196
Scaling      60 70 292
Scattering      35 176
Scattering line shape      37
Self-affine      206
Self-avoiding polymer      134 149 326
Self-similarity      59 164 196
Sequence alignment      240
Sign transition      234
Sine-Gordon model      183 186 350
Spanning tree      333
Spin glass      210 233
Spin wave      48 168 278
Spinodal      14 262
Spontaneous symmetry breaking      29 131
Square lattice      98 112
Stability      7 23
Stanley      163
Star-triangle transformation      153 155
Stationary      202 208
strain      7 175
Strong localization      241
Superconductor      48 49 285
Superfluid      21 29 33 39 173
Superfluidity      29
Surface growth      204
Surface tension      16 49 197 283
Surfactant      16
susceptibility      37 78
Symmetry      22
Symmetry, translation      7
Symplectic matrix      247
Thermodynamic limit      2 9
Thin film      17
Thouless      177
Time reversal      247
Time-dependent Landau — Ginzburg equation      192
Topological defect      162 165
Transfer matrix      101 107 116 118 135 216 217 322
Transition probability      115 122
Translation      7 174 204
Transverse      8 36 175
Transverse susceptibility      28 33 39 49 282
Triangular lattice      108
Tricritical exponents      33 273
Tricritical point      32 50 100 271 287
Tunneling      242
Uniformity      21
Unitary matrix      247
Universal      6 19
Universality      66 92 98
1 2
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