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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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283 22 24 326 159 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 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 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 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 158 230 264 Dihedral group 278 Dihedral group 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 19 Finite group, dihedral 158 Finite group, permutation 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 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 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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