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Henkel M. — Conformal Invariance and Critical Phenomena
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Название: Conformal Invariance and Critical PhenomenaАвтор: 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: Рубрика: Физика /Термодинамика, статистическая физика /Квантовые методы /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1999Количество страниц: 433Добавлена в каталог: 10.09.2005Операции: Положить на полку |
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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 286 Null operator, explicit for 287 Null vector, null operator 92 O(n) model 22 240 259 260 326 332 O(n) model, 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, 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 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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