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Christe P., Henkel M. — Introduction to conformal invariance and its applications to critical phenomena
Christe P., Henkel M. — Introduction to conformal invariance and its applications to critical phenomena



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Название: Introduction to conformal invariance and its applications to critical phenomena

Авторы: Christe P., Henkel M.

Аннотация:

This book grew from a series of lectures given to graduate students of condenses matter physics. This introduction to conformal invariance and to two-dimensional critical phenomena reflects their theoretical background. The algebraic foundation of critical theories in two dimensions is introduced and explained as is the role of modular invariance for the partition function. A large part of the book is devoted to numerical methods and their application in various models. Finite-size scaling techniques and their conformal extensions are treated in detail. Transfer matrix diagonalization methods are used to study, among others, the Ising and Potts models, including tricritical behaviour, the Ashkin-Teller model systems with continuous symmetries such as the XY model and the XXZ quantum chain as well as the Yang-Lee edge singularity. Numerical methods also make it possible to describe the vicinity of the critical point. The exact S-matrix approach, truncation method, the thermodynamic Bethe ansatz and the asymptotic finite-size scaling function technique are illustrated on simple models. The integrability of the two-dimensional Ising model in a magnetic field is dealt with. Finally, the extension of conformal invariance appropriate to the study of surface critical phenomena and defect line problems is described, and the book closes with an outlook towards possible applications in critical dynamics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 276

Добавлена в каталог: 15.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C$-parity      108
$c$-theorem      187
$N$-shift technique      119
$O(n)$ model      15 166 170 221 225
$S$-matrix      193 213
$\epsilon$-expansion      9 15 221
$\sigma-\Gamma$ algebra      108
ADE classification      139 152
Affine extension      see Kac — Moody algebra
Affine Lie algebra      see Kac — Moody algebra
Affine Toda theory      199
Amplitude-exponent relation      48 224 234
Amplitude-exponent relation, in 3D      168-169
Amplitude-exponent relation, non-linear      190
Anisotropy exponent      242
Anomalous thresholds      195
Anomaly      34
Ashkin — Teller model      157 205 231
Ashkin — Teller model, operator content      161
Ashkin — Teller model, quantum chain phase diagram      159
Ashkin — Teller model, surface operator content      231
Associativity of the OPE      69
Average value      3 244
Block spin      4
Blume — Capel model      149
BMKD algorithm      115
Boltzmann constant      3
Boltzmann weight      16
Bootstrap equation      195
Bound states      195
BST algorithm      119
Bulk scaling amplitudes      187
Callan — Symanzik beta function      163 188
Casimir effect      37 50
Central charge      33 50 88 237
Central charge, Ising model      130 227
Central extension      see Central charge
Charge conjugation operator      108 157
Charge operator      108
Charge sector      108
Clock model      14
Compactification circle      143
Compactification orbifold      145 157
Compactification radius      143
Conformal anomaly      see Central charge
Conformal block      68 (see also Conformal tower)
Conformal group      24
Conformal normalization      126 172 225 230
Conformal perturbation theory      172
Conformal tower      112 131 173 175
Conformal transformations projective      26 29 221
Conformal weights      27 144
Conservation law      191-192
Conservation law, absence for $\phi_{22}$ perturbation      203
Conservation law, stress-energy tensor      32
Convergence of finite-size amplitudes      115
Convergence of finite-size sequences, linear      118
Convergence of finite-size sequences, logarithmic      118
Corner exponents      241
Correlation function      see Two- three- four-point
Correlation functions, differential equation      58
correlation length      3 22 42 150 187
Coulomb gas      84 89
Counting criterion      191
Coxeter exponents      199
Coxeter number      139 199
Critical exponents      4 14 149 220
Critical exponents, finite-size estimates      111
Crossing condition      68 195
Dangerous irrelevant scaling field      6 42
Defect line      233
Defect line exponents      233
Defect strength      233
Detailed balance      244
Dihedral group $D_{4}$      173
Dihedral group $D_{4}$, irreducible representations      158
Directed percolation      120 245
Discretized energy and momentum      128
Disorder line      125 246
Droplet picture      2
Dual lattice      11
Dual site      12
Duality      11 102 104 109 125
Dynamical exponent      242
Dynamical scaling function      242
Dynamical symmetry      101 153 224
Dynkin diagram      16
Elastic scattering      193
Euler pentagonal theorem      141
Extraordinary transition      218
Extrapolation length      218
Extreme anisotropic limit      see Hamiltonian limit
Fermion number operator      123
Finite-lattice extrapolation      117
Finite-size corrections      132 173 177
Finite-size corrections, from conformal tower of the identity      176
Finite-size scaling      39 42 182 224
Finite-size scaling amplitude      44 128
Finite-size scaling functions      133 179-180 182 213
Finite-size scaling limit      41 174
Finite-size scaling region      40-41
Finite-size scaling variables      44 174
Fluctuation-dissipation theorem      6
Four-point function      30 59 67 76 79-80 82 89-90
Free boson      84 141
Free boundary conditions      38 226
Free energy      3 5 22 38 42 49 104 128 187 221
Free energy, surface      217
Fuchs differential operator      74
Generating function of the partitions of the integers      127
Global symmetry      109 122
Half-partition function      167
Hamiltonian limit      95 100 107 157
Highest weight of Virasoro algebra representations      52
Hubbard-Stratonovi$\acute{c}$ transformation      97
Hypergeometric function      75 77 90 178
Hyperscaling      6 221
IRF model      16
Irrelevant scaling field      5 45 173
Ising metamagnet      150
Ising model      1 17 60 76 94 115 122 142 169 173 176 180 192 197 200 214 225 234
Ising model, operator content      132
Ising model, operator content with a defect line      240
Ising model, quantum chain phase diagram      125
Ising model, surface operator content      228
Ising quantum chain      96 122 201 234
Ising quantum chain, diagonalization      123 226 234
Jordan — Wigner transformation      123
Kac formula      60 88 126 153 155
Kac table      see Kac formula
Kac — Moody algebra      85 238-239
Kac — Moody algebra, shifted      232 240
Kinetic Ising model      245
Lanczos algorithm      112
Latent heat      42 110
Lattice momentum      112
Level of Kac — Moody algebra      85
Level of Virasoro algebra representation      53 126
Lie superalgebra      152
Lieb, Schultz, Mattis technique      124 226 235
Logarithmic transformation      47 224 234
Loop algebra      26
Magnetic field      1 200 203
Magnetic field, complex      8
magnetization      see Order parameter
Majority rule      4
Marginal scaling field      5 87 234
Master equation      244
Metric factors      42
Minimal $S$-matrix      196 214
Minimal models      56 60-61
Minimal models, non-unitary      155
Minimal models, unitary      60 139 166
Modular group      137
Modular invariance      137 168
Modular transformation      141
monodromy      70 72 82
Multicritical Ising models      205
Neutrality condition Coulomb gas      86
Non-linear scaling field      45
Normal ordering      85 134 236
Null operator      54
One-fermion energies      124
Ope      see Operator product expansion
Operator product algebra      179 (see also Operator product expansion)
Operator product algebra hypothesis      65
Operator product expansion      51 65 76 83 86 90 142 172 182
Operator product expansion, coefficients      78 82-83 91
Orbifold      145
Order parameter      3 42 110
Ordinary transition      218
Orthosymplectic Lie superalgebra      153
Parity operator      108
Parity sector      108
Partition function      3 138-139 141-142 145-146 166
Pauli matrices      96
Periodic boundary conditions      38
Persistence length      150
Phenomenological renormalization      45 150
Poisson resummation formula      141
Potts model      10 14 17 61 101 107 146 148 156 166 173 177 228-229 231 233
Potts model, operator content      148
Potts model, surface operator content      228
Primary      28 45 51 86 243
Projective invariant      30
Quantum Hamiltonian      20 95
Quasi-primary      27 52 54 192 243
Rapidity      193
Reaction-diffusion process      242 246
Reduced magnetic field      3
Reduced surface magnetic field      219
Reduced temperature      3
Relevant scaling field      5 173
Remnant function      133 181
Renormalization group      4
Renormalization group eigenvalue      5
Roomany — Wyld approximant      163
Rounding exponent      40
Rounding temperature      40
RSOS model      16
Scalar $\phi^{4}$ theory      see Ising model
Scale invariance      24 222
Scaling dimension      7 27
Scaling field      5
Scaling operator      7
Scaling relations      6 221
Schr$\ddot{o}$dinger group      242
Schwarzian derivative      37
Screening current Coulomb gas      88
secondary      28 45
Shift exponent      40
Singular exponents      72
Singular regular points      74
Slab geometry      217
Special conformal transformation      24 222
Special transition      218
Specific heat      3 42 109
Spherical model      15 115 169
Spin      27
Stress-energy tensor      31 52 85 87 239
Strip geometry      37 47 49 107
Strongly anisotropic system      242
Sum rule, central charge      189
Sum rule, conformal weights      74
Superconformal algebra      153
Superconformal characters      153
Superconformal invariance      152 231
Supersymmetry      152
Surface exponents      220
Surface thermodynamics, excess quantity      219
Surface thermodynamics, local quantity      219
Surface thermodynamics, mixed quantity      220
Surface transition      218
susceptibility      3 42 110
Temperley — Lieb algebra      103 229
Thermodynamic Bethe ansatz      207
Three-dimensional systems      168
Three-point function      30 66 172 174 243
Toroidal boundary conditions      111 122 159
Torus      137
Transfer matrix      19 94
Transverse field, Ising model      96
Tricritical Ising model      9 149 173 203
Tricritical Ising model, operator content      151
Tricritical Ising model, surface operator content      230
Truncation method      183 216
Two-point Function      3 29 47 55 84 86 171 174 220-221 226 243
Two-point function, scaling      6 242
Unitarity      56 60
Unitarity, scattering      194
Universality      3 18 42-43 100 129 133 182
Universality classes      3 14
VBS algorithm      118
Verlinde formula      142
Verma module      52-53 62
Verma module, degenerate      54 57
Vertex operator      86 143
Virasoro algebra      36 51 88
Virasoro character      63 126 155
Virasoro character, for $c=1$      161
Virasoro character, generic      53
Virasoro character, modular transformation      139
Virasoro generators      34 134 236
Virasoro generators, Hermiticity      55
Ward identity      29 32 86 223
XXZ quantum chain      165 229 232
XXZ quantum chain, operator content      165
XXZ quantum chain, relation to other spin systems      158 165 229 232
XXZ quantum chain, surface operator content      232
XY model      15 144 162 231
Yang — Lee singularity      8 61 154 156 183
Yang — Lee singularity, operator content      156
Yang — Lee singularity, surface operator content      230
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