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Henkel M. — Conformal Invariance and Critical Phenomena
Henkel M. — Conformal Invariance and Critical Phenomena



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Название: Conformal Invariance and Critical Phenomena

Автор: Henkel M.

Аннотация:

This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are reviewed.


Язык: en

Рубрика: Физика/Термодинамика, статистическая физика/Квантовые методы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 433

Добавлена в каталог: 10.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Minimal models, non-unitary      227 245 257
Minimal models, unitary      94 207 240
Minimal S-matrix      293 317
Modular group      205
Modular invariance      206 258
Modular transformation      209
Moebius transformation      48
monodromy      110 112 124 135
Monodromy matrix      110 111 119 126
Monodromy transformation      119 126
Multicritical Ising models      154 313
N-shift technique      174
Navier — Stokes equation      254
Neutrality condition, Coulomb gas      131
Non-linear scaling field      71
Normal ordering      129 201 354
Normal transition      335 see
Null operator      87 92 97 101 287
Null operator, differential equation for level 2      103
Null operator, differential equation for level 4      116
Null operator, explicit for $\phi_{1,2}$, $\phi_{1,3}$, $\phi_{2,2}$      286
Null operator, explicit for $\phi_{1,s}$      287
Null vector, null operator      92
O(n) model      22 240 259 260 326 332
O(n) model, $n \rightarrow 0$ limit and polymers      26 284
One-fermion energies      186
Ope      see "Operator product expansion"
Operator product algebra      270 see
Operator product algebra hypothesis      105
Operator product expansion      84 101 118 125 135 156 211 256 262 274 283
Operator product expansion, coefficients      52 120 124 125 137 140 272
Orbifold      213 360
Orbifold models      212 215 230 see
Order parameter      5 68 160 349
Order parameter, staggered      15
Ordinary transition      322 332
Orthosymplectic Lie superalgebra      225
Parastatistics      82
Parity operator      158
Parity sector      158
Partition function      5 206 208 209 214 215 239
Partition function, modular invariant      207
Pauli matrices      143
Percolation      24 34 81 245 250 273 344
Percolation, bond      25
Percolation, critical exponents      26
Percolation, crossing probability      344
Percolation, directed      176 371
Percolation, incipient spanning cluster      346
Percolation, operator content      247
Percolation, relation to Potts model      25
Percolation, site      25
Percolation, surface operator content      343
Period-doubling sequence      363
Periodic boundary conditions      64 74 162
Persistence length      222
Persistent current      363 364
Persistent current, defect      364
Persistent current, parity effect      366
Phase ordering kinetics      370
Phenomenological renormalization      72 222
Physisorption      31
Poisson resummation formula      209
Polymer      26 35 247 250 284 346
Polymer, branched      see "Lattice animal"
Polymer, relation to O(n) spin model      26 284
Potts model      17 19 35 95 96 139 151 153 157 214 219 229 240 264 268 273 304 337—339 341 343
Potts model, $q \rightarrow 1$ limit      25
Potts model, chiral      19 20 35 306
Potts model, operator content      219
Potts model, relation to lattice animals      252
Potts model, relation with RSOS model      30
Potts model, surface operator content      337
Potts model, two-point function      182
Potts model, vector      19
Primary      50 72 84 131
Profile      346
Profile, non-diagonal      349
Projective invariant      52 328
Quantum chain      14 143 147
Quantum chain at finite temperature      77 82 278
Quantum chain, central charge      77 241
Quantum Hamiltonian      14 39 141 143 383
Quasi-primary      49 86 88 244 288 373
Quasiperiodic modulation      362
Radial quantization      89
Radius of gyration      27 284
Random Ising model      349
Rapidity      290
Reaction-diffusion process      383
Reduced magnetic field      4
Reduced surface magnetic field      324
Reduced temperature      4
Relevant      see "Scaling field"
Relevant scaling field      264
Remnant function      198 272
Renormalization group      11 52
Renormalization group eigenvalue      7
Renormalization group trajectory      52 280 314
Response field      371
Response function      370 376
Reynolds number      254
Rocha — Caridi formula      99 189 246
Roomany — Wyld approximant      237
Rotation      45 46
Rounding exponent      65
Rounding temperature      65
RSOS model      27 28 95 96 156 300
S-matrix      289 316
SAW      see "Self-avoiding walk"
Scalar $\phi^{4}$ theory      145 146 see
Scale invariance      4 6 328 375 377
Scaling amplitude ratios      304
Scaling dimension      7 12 48
Scaling field      7
Scaling field, dangerously irrelevant      10
Scaling field, irrelevant      9
Scaling field, marginal      9
Scaling field, relevant      9
Scaling function      9
Scaling operator      7 12
Scaling operator, covariance      43 49
Scaling relations      10
Scaling relations, anisotropic      20 42
Scaling relations, surface      326
Scaling relations, tricritical      42
Schroedinger group      372
Schroedinger invariance      373—376 382
Schwarzian derivative      60
Screening charges      133
Screening current, Coulomb gas      133
secondary      50 71
Self-avoiding walk      26 248 249
Self-avoiding walk, oriented      307
Self-duality      18 67 153 159 181 188 305
Sequence extrapolation      173
Shift exponent      65 79 80 82
Shift exponent, effective      81
Singular exponent (ODE)      112
Singular regular point (ODE)      114
Slab geometry      321
Special conformal transformation      45 46 327
Special transition      322 358
Specific heat      5 68 78 160
Specific heat, amplitudes and self-duality      67 305
Spectral parameter      216
Spherical model      22 82 171 245 260
Spin      48
Stream function      255
Stress-energy tensor      see "Energy-momentum tensor"
Strip geometry      61 74 76 82 157 331
Strong embedding      251 252
Strongly anisotropic system      369
Substitution matrix      362
substitution sequence      362
Sugawara form      129
Sum rule, central charge      282
Sum rule, conformal weights      114 283
Summary of steps of conformal invariance applied to a given model      203
Superconformal algebra      225
Superconformal characters      225
Superconformal invariance      224 341
Superconformal invariance and percolation      246
Supersymmetry      224 253
Surface exponent      324
Surface exponent, energy density      332
Surface magnetic field      322
Surface magnetization      362
Surface thermodynamics, excess quantity      324
Surface thermodynamics, local quantity      324
Surface thermodynamics, mixed quantity      324
Surface transition      323
susceptibility      5 68 160 237 241 283
Temperley — Lieb algebra      150 153 338
Theta point      27 35 250—252
Three-dimensional systems      258
Three-point function      52 106 228 243 262 265 374
Tight-binding model      364
Toroidal boundary conditions      162 183 232
Torus      205
Transfer matrix      38 142 218 245 249 344
Translation      45 46 181
Translation invariance      162
Transverse field      14 143
Tricritical exponents      42
Tricritical Ising model      14—16 221 264 273 311
Tricritical Ising model, operator content      223
Tricritical Ising model, surface operator content      340
Tricritical point      15
Tricritical point, non-unitary      229
Tricritical Potts model      19 35
Truncation method      275 318
Two-point Function      5 51 74 82 90 127 128 131 228 242 243 245 261 265 325 326 328 333 360 367 370 374 379 381
Two-point function for quantum chains at finite temperature      278
Two-point function, scaling      12 327 369
Unitarity      90 94 97 225
Unitarity, scattering      291
Unitary minimal series      94
Universality      4 33 37 68 70 148 192 198 258 272 274 384
Universality classes      4 20 see
Upper critical dimension      10
Vacancy operator      270
VACUUM      88
Vanishing curves      91 94
VBS algorithm      174
Verlinde formula      211
Verma module      85 86 97
Verma module, degenerate      87 92
Vertex operator      131 211
Virasoro algebra      60 83 133
Virasoro character      97—99 189 228
Virasoro character for c = 1      234
Virasoro character, generic      87
Virasoro character, modular transformation      207
Virasoro character, numerical computation      190
Virasoro generators      57 201 204 354 356
Virasoro generators, Hermiticity      89
Vorticity      254
W symmetry      221
Wandering exponent      362
Ward identity      44 51 54 55 131 329 347
Ward identity, projective      51 243 244 327 373 379
Watermelon topology      247
Wright formula      380
XXZ quantum chain      238 338 342
XXZ quantum chain, operator content      239
XXZ quantum chain, relation to nonequilibrium systems      384
XXZ quantum chain, relation to other spin systems      231 239 339 342
XXZ quantum chain, surface operator content      342
XY model      21 22 34 212 213 236 260 341
XY quantum spin model      183 188 191 198 258 267 272 383
Yang — Baxter equation      291
Yang — Lee singularity      23 24 96 227 229 253 256 276
Yang — Lee singularity, operator content      229
Yang — Lee singularity, surface operator content      340
Zamolodchikov counting criterion      287 288
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