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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
$\delta$-theorem      283
$\epsilon$-expansion      22 24 326
$\sigma-\Gamma$ algebra      159
ADE classification      207 223
ADE model      216 300
ADE model from Dynkin diagram      29
ADE model, dilute      217 301
ADE model, dilute, free energy for $A_{3}$ model      301
ADE model, dilute, order parameter      301
ADE model, order parameter      300
ADE model, related models      29
Adjacency matrix      28 216
Affine extension      see "Kac — Moody algebra"
Affine Lie algebra      see "Kac — Moody algebra"
Affine Toda theory      296
Amplitude      see "Critical amplitude"
Amplitude-exponent relation      75 331 351 361
Amplitude-exponent relation in 3D      258 259
Amplitude-exponent relation, non-linear      283
Anisotropic local scaling      377
Anisotropy exponent      20 42 369
ANNNI model      369
ANNNO(n) model      370
ANNNS model      370 381 382
Anomalous thresholds      292
Anomaly      57
Antiferromagnet      336
Aperiodic modulation      362
Arnoldi algorithm      170
Ashkin — Teller model      230 313 340
Ashkin — Teller model, operator content      234
Ashkin — Teller model, quantum chain phase diagram      233
Ashkin — Teller model, relation to defect line      360
Ashkin — Teller model, surface operator content      340
Associativity of the OPE      108
Average value      5 375
beta function      236
Bethe ansatz equations      302
Block spin      11
Blume — Capel model      16 221
BMKD algorithm      169
Boltzmann constant      4
Boltzmann weight      28
Bootstrap equation      292
Bound states      292
Boundary operator      345
BST algorithm      174
Bulk scaling amplitudes      279
C-parity      159
c-theorem      280 281
Callan — Symanzik beta function      236 281
Cappelli — Itzykson — Zuber — Kato theorem      207
Casimir effect      61 77
Central charge      56 77 78 331 354
Central charge of Coulomb gas      133
Central charge, c, from specific heat      77
Central charge, effective      228
Central charge, free boson      78 130
Central charge, Ising model      193 335
Central charge, k, from susceptibility      241
Central extension      see "Central charge"
CHARACTER      87 88 97—99 189
Charge conjugation operator      158 230
Charge operator      158
Charge sector      158
Charge U(1)      131 248 308
Chemisorption      31
Circle models      212
Classification of modular invariant partition functions, minimal models with c < 1      207
Classification of modular invariant partition functions, models with c = 1      215
Clock model      19
Column geometry      259
Compactification radius      212
Compactification, circle      212
Compactification, orbifold      213 230
Conformal algebra, generators      47 62 242 327
Conformal anomaly      see "Central charge"
Conformal block      108 see
Conformal group      45
Conformal group, analytic functions      46
Conformal invariance      4 49 54 326 351
Conformal normalization      163 188 199 262 332 339 359
Conformal perturbation theory      263
Conformal tower      85 86 163 194 263 266 354 359
Conformal transformations      45
Conformal transformations, angle-preserving      45
Conformal transformations, projective      48 51 244 326
Conformal turbulence      254
Conformal turbulence, minimal model      257
Conformal weights      48 213
Conservation law      287 288
Conservation law, absence for $\phi_{22}$ perturbation      313
Conservation law, energy-momentum tensor      55
Convergence of DMRG algorithm      181
Convergence of finite-size amplitudes      171
Convergence of finite-size sequences, linear      173
Convergence of finite-size sequences, logarithmic      173
Convergence of Lanczos algorithm      168
Corner exponent      367
Correction exponent $\omega$      72 81 156 264
Correlation function      see "Two-point function" "Three-point "Four-point
Correlation functions, covariance      7 44 49
Correlation functions, differential equation      103
correlation length      2 5 41 68 222 279
Coulomb gas      127 248 309
Coulomb gas and minimal models      134
Coulomb gas, correlators      134
Coulomb gas, screened      132 134
Coxeter exponents      29 209 296
Coxeter number      29 209 216 296
Critical amplitude      67 304
Critical amplitude, universal ratio      304
Critical dynamics      370
Critical exponents      6 21 220 324
Critical exponents, bulk      6
Critical exponents, definition      6
Critical exponents, finite-size estimates      162 331
Critical exponents, non-equilibrium      384
Critical exponents, surface      324
Critical exponents, tricritical      15
Critical point      3
Cross-over exponent      363
Crossing condition      107 108 120 292
Dangerous irrelevant scaling field      68
Defect line      350
Defect line exponents      350
Defect strength      350
Density matrix renormalization group      177
Detailed balance      375
Dihedral group      158
Dihedral group $\mathbb{D}_{4}$      158 230 264
Dihedral group $\mathbb{D}_{4}$ and breaking of rotation invariance on square lattice      278
Dihedral group $\mathbb{D}_{4}$, irreducible representations      232
Dilatation      11 45 46
Dipolar interactions      13 32
Directed percolation      176 371
Discretized energy and momentum      148 163 191
Disorder line      187 199 259 383
dispersion relation      77 163 188 196 244 380 382
DMRG algorithm      177
DMRG algorithm, finite system      179
DMRG algorithm, infinite system      178
Droplet picture      3
Dual bond      18
Dual coupling      18
Dual lattice      18
Dual site      18
Duality      17 20 67 151 153 159 182 188
Dynamical exponent      370 see
Dynamical scaling function      371
Dynamical symmetry      83 148 225 331
Dynkin diagram      28
Eigenvalues      167
Eigenvectors      168
Elastic scattering      289
Energy density on the lattice      242
Energy density, surface exponent      332
Energy spectrum, turbulence      255
Energy-momentum tensor      54 86 129 133 280 356 374
Enstrophy      255—257
Euler pentagonal theorem      209
Euler relation      18
Experiment      2 3 13 14 21
Experiment, bulk exponents in 2D      30
Experiment, central charge      241
Experiment, classical 2D and quantum (1+1)D systems      14
Experiment, finite-size scaling in 2D      81
Experiment, finite-size scaling in 3D      78
Experiment, reaction-diffusion in 1D      375 384
Experiment, surface exponents in 3D      326
Experiment, Yang — Lee zeroes      23
EXPONENT      see "Critical exponents"
Exponent inequalities      10
Extended conformal algebras      226
Extraordinary transition      323 333 335 368
Extrapolation algorithms      see "BST-algorithm" "VBS-algorithm"
Extrapolation length      322
Extreme anisotropic limit      see "Hamiltonian limit"
Fermion number operator      184
Fibonacci sequence      362
Finite group, cyclic $\mathbb{Z}_{p}$      19
Finite group, dihedral $\mathbb{D}_{p}$      158
Finite group, permutation $\mathbb{S}_{p}$      17
Finite sizes, relation to inverse temperature      40
Finite-lattice extrapolation      173
Finite-size corrections      71 197 263 268
Finite-size corrections from conformal tower of the identity      266
Finite-size scaling      63—68 75 77 161 162 274 330
Finite-size scaling amplitude      70 75 191 259 331 334 337
Finite-size scaling functions      70 197 198 270—272 274 298 312 316
Finite-size scaling limit      67 264
Finite-size scaling region      65 67
Finite-size scaling variables      70 264
First intersection      94
Fixed point      11
Fluctuation-dissipation theorem      7 370
Form factor      304
Four-point function      52 103 107 117 120 122 124 134 136 137
Free boson      78 127 209 see
Free boundary conditions      64 78 162 333
Free energy      5 40 63 68 76 191 279 301 322 325
Free energy density      7
Free energy, surface      64 322
Free fermion      82 see
Free Parisi — Sourlas field theory      254
Friedan — Qiu — Shenker theorem      94
Frobenius series      116
Fuchs differential operator      114
Fuchs theorem      116
Galilei invariance      373
Generating function of lattice animals      251
Generating function of polymers      27 250
Generating function of the partitions of the integers      189
Geometric phase transition      24
Glauber dynamics      375 383
Global symmetry      17 19 21 158 160 184 221 229 230 232 338
Goddard — Kent — Olive theorem      97
Half-filling      364
Half-partition function      240
Hamiltonian limit      141 143 147 157 230
Heisenberg model      22 80 241 260
Highest weight of Kac — Moody algebra      131
Highest weight of superconformal algebra      225
Highest weight of Virasoro algebra representations      85
Hilhorst — van Leeuwen model      361 367
history      13 31
Hubbard — Stratonovich transformation      144
Hypergeometric function      115 116 118 126 135 140 269
Hypergeometric function, asymptotics      380
Hyperscaling      10 20 69 70 325
Hyperuniversality      70
Ideal bose gas      78
Ideal Fermi gas      82
Integrability      288
IRF model      28 216
Irrelevant      see "Scaling field"
Irrelevant scaling field      71 263
Ising lattice gas      13
Ising metamagnet      16 221
Ising model      1 13 34 35 95 117 139 141 171 183 210 240 242 258 264 267 271 272 288 294 297 298 305 317 332 336 351
Ising model, (1+1)D      see "Ising quantum chain"
Ising model, (2+1)D      161 258
Ising model, antiferromagnetic      336
Ising model, in magnetic field at $T_{c}$      288 296 298 301
Ising model, operator content      196
Ising model, operator content with a defect line      357
Ising model, random      349
Ising model, relation with diluted $A_{3}$ model      301
Ising model, relation with RSOS model      30
Ising model, surface operator content      335
Ising quantum chain      14 143 147 183 245 298 351
Ising quantum chain, aperiodic      362
Ising quantum chain, diagonalization      184 333 352
Ising quantum chain, Glauber dynamics in 1D      383
Ising quantum chain, multispin interactions      181
Ising quantum chain, phase diagram      187
Ising quantum chain, spin S = 1      198
Ising uniaxial magnet      13
Jordan — Wigner transformation      184
Kac formula      93 96 97 155 156 189 227
Kac formula from Coulomb gas      133
Kac formula, non-unitary      227
Kac formula, superconformal      225
Kac table      see "Kac formula"
Kac — Moody algebra      28 129 216 241 355 356
Kac — Moody algebra, shifted      342 357
Kinetic Ising model      375 383
Kinetic spherical model      376
Lanczos algorithm      163—169
Lanczos algorithm, convergence      167
Lanczos algorithm, Fortran code      164
Lanczos algorithm, re-orthogonalization      168
Landau — Ginzburg — Wilson      146 154
Latent heat      68 161
Lattice animal      251 367
Lattice momentum      149 162
Level of Kac — Moody algebra      129
Level of Virasoro algebra representation      85 87 189
Lie superalgebra      224
Lieb, Schultz, Mattis technique      185 333 352
Lifshitz point      370 381
Local scale invariance      371 377
Logarithmic operators      243
Logarithmic transformation      74 149 331 351
Loop algebra      47
Luck criterion      362 363
Magnetic field      1 298 311
Magnetic field, complex      23
Magnetic field, staggered      14
magnetization      see "Order parameter"
Manhattan lattice      310
Marginal      see "Scaling field"
Marginal scaling field      286 308 351
Mass ratios from factorizable S-matrix      294—297
Mass ratios, numerical      300 302 313 316
Mass term      373 378
Master equation      375
Metamagnet      16
Metric factor      68 198 331
Minimal models      90 93 96 134
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