Baxter R.J. — Exactly Solved Models in Statistical Mechanics :: Электронная библиотека попечительского совета мехмата МГУ

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Baxter R.J. — Exactly Solved Models in Statistical Mechanics

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Название: Exactly Solved Models in Statistical Mechanics

Автор: Baxter R.J.

Аннотация:

This text explores the solution of two-dimensional lattice models. Topics include basic statistical mechanics, Ising models, the mean field model, the spherical model, ice-type models, corner transfer matrices, hard hexagonal models, and elliptic functions.

Язык:

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1982

Количество страниц: 486

Добавлена в каталог: 16.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$Z_{N}$ model      322
Anti-ferroelectric phase of eight-vertex model      246
Anti-ferroelectric phase of ice-type model      152
Ashkin — Teller model      254 353—362
Asymptotic degeneracy of maximum, eigenvalues of the transfer matrix      111—114 152—153 239— 240
Bethe ansatz      139 168
Bethe lattice      13 47—59 306—309 351
Cayley tree      47—49
Coexistence curve      29
Commuting transfer matrices      see also Commuting transfer matrices star-triangle
Commuting transfer matrices, eight-vertex model      214
Commuting transfer matrices, general two dimensional IRF model      370—372
Commuting transfer matrices, hard hexagon model      452
Commuting transfer matrices, ice-type model      180—181 185—186
Commuting transfer matrices, planar Ising model      85—86 96
Corner transfer matrices      363—401
Corner transfer matrices, eight-vertex model      385—389
Corner transfer matrices, hard hexagon model      405—407 426— 432
correlation length      19
Correlation length, eight-vertex model      241—243 284
Correlation length, hard hexagon model      452
Correlation length, ice-type model      154—155
Correlation length, one-dimensional Ising model      36
Correlation length, planar Ising model      118 120
Correlation length, relation to the eigenvalues of the transfer matrix      36 115—118
Correlations      10 18—19
Correlations, one-dimensional Ising model      35—36
Correlations, planar Ising model      297—298
Critical exponents      4 17 19 20 29
Critical exponents, Ashkin — Teller model      360—361
Critical exponents, Bethe lattice Ising model      58
Critical exponents, classical values      30—31
Critical exponents, continuously variable      8 253—254 361
Critical exponents, eight-vertex model      253—255
Critical exponents, hard hexagon model      448—452
Critical exponents, ice-type model      157 160 165
Critical exponents, mean-field Ising model      44 46
Critical exponents, one-dimensional Ising model      38
Critical exponents, planar Ising model      122
Critical exponents, Potts model      351—352
Critical exponents, spherical model      69—71
Critical exponents, three-spin model      320—321
Critical point      3 10 28
Critical point, Ashkin — Teller model      359—362
Critical point, Bethe lattice Ising model      54 307— 308
Critical point, eight-vertex model      248
Critical point, hard hexagon model      405 447 449
Critical point, ice-type model      156
Critical point, mean field Ising model      44
Critical point, numerical values for the isotropic Ising model      77 308
Critical point, one-dimensional Ising model      37
Critical point, planar Ising model      77—78 87 120—121 307—308
Critical point, Potts model      338—339 347—348
Critical point, spherical model      67
Critical point, three-spin model      314
Curie point      2 44
Dichromatic polynomial      324
Difference kernel, transformation to      145 171
Dimer problem      124—126
Disorder points      247
Dual lattice      74 79
Duality, Ashkin — Teller model      357
Duality, eight-vertex model      206
Duality, planar Ising model      73—80 86—87
Duality, Potts model      338 346
Eight-vertex model      202—321
Eight-vertex model, ‘electric’ arrow formulation      202— 204 276—279
Eight-vertex model, ‘magnetic’ spin formulation      207— 210 286—289
Elliptic functions      455—473
Elliptic functions, conjugate modulus identities      419 444 446 467—468
Elliptic functions, in eight-vertex model      212—215
Elliptic functions, in hard hexagon model      412—415
Elliptic functions, in planar Ising model      102—103
Elliptic functions, in square-lattice four-colouring problem      171—176
F model      129
Ferroelectric ice-type model in a field      160—165
Ferroelectric phase of eight-vertex model      246
Ferroelectric phase of ice-type model      151
Four colour problem      331—332
Free energy      16—17
Free energy, Bethe lattice Ising model      55—56 59 306
Free energy, critical Potts model      339—340 348- 350
Free energy, eight-vertex model      236—237 285— 286
Free energy, hard hexagon model      408 426 444 450
Free energy, ice-type model      145—150
Free energy, inversion relation for      see inversion relations
Free energy, mean field Ising model      42
Free energy, one-dimensional Ising model      34
Free energy, planar Ising model      110—111 296— 306
Free energy, spherical model      61—64
Free energy, three-spin model      319—320
Free-fermion model      270—271 310
Hard hexagon model      402—454
Heisenberg chain      see XYZ chain
Hyperbolic trigonometry and the star- triangle relation      292
Hyperscaling      7
Ice model      127—129 148

Ice-type model      127—201
Interfacial tension      20 110—114 152 153 239—241 452
Internal energy      9 16
Internal energy, critical Potts model      344—345 349— 351
Internal energy, spherical model      64
Inversion relations for local transfer matrices, free energy, and corner transfer matrices      383— 387 421—423 427-429
Ising model      19—32 (see also specific properties e.g.
Ising model, Bethe lattice      13 47—59 306—309
Ising model, mean field      13 39—46
Ising model, one-dimensional      12 32—38
Ising model, planar      72—126 294—309
Ising model, relation of d-dimensional model to a (d-1)-dimensional quantum- mechanical model      266—267
Kagom $\acute{e}$ lattice      276—277
KDP model      129
Landen transformation      466—467
Latent heat of Potts model      345 349—351
Lattice gas      24—30
Lattice gas, hard hexagons      402 409
Lattice gas, mean field      46
Liouville’s theorem      458
Local transfer matrices $U_{i}$ , edge transfer matrices for the planar Ising model      84—85 124
Local transfer matrices $U_{i}$ , face transfer matrices for the general two-dimensional IRF model, and for the hard hexagon model      369 421
Local transfer matrices $U_{i}$ , inversion relations for      see inversion relations
Local transfer matrices $U_{i}$ , vertex transfer matrices for the ice-type and eight-vertex models      188
magnetization      1—4 17 21—23
Magnetization, Bethe lattice Ising model      52—54 59
Magnetization, mean-field Ising model      41
Magnetization, one dimensional Ising model      34
Magnetization, spherical model      64
Mean-field model      13 39—46
Medial graph      325 332—333 345—346
One-dimensional Ising model      12 32—38
Order parameter      see also spontaneous magnetization and spontaneous polarization
Order parameter, hard hexagon model      404 438 442 446 451
Pair-propagation through a vertex      194 215
Partition function      8—9 16 25
Partition function, per site      see free energy
Percolation problem      324
Pfaffian      125
Phase transition      1—3 (see also critical point)
Poisson summation formula      468—469
Polarization      see also spontaneous polarization
Polarization, ferroelectric ice-type model      162—165
Potts model      322—352
Renormalization group      11
Rogers — Ramanujan and related identities      434—443
Scaling hypothesis      4—7 37
Scaling hypothesis, full verification for the one-dimensional Ising, mean-field Ising, Bethe lattice Ising, spherical and ferroelectric ice-type models      37 46 58 71 165
Scaling relations between critical exponents      6 20 21
Scaling relations between critical exponents, verification of ( $\alpha,\mu,\nu$ ) relations for the planar Ising, ice-type, eight- vertex, three-spin and hard hexagon models      122 160 253 321 452
Scaling relations between critical exponents, verifications for other models      see scaling hypothesis
Series expansions      10 22—23 395—396 404
Six-vertex model      see ice-type model
Specific heat      16
Spherical model      13 60—71
Spontaneous magnetization      1—4 23
Spontaneous magnetization, Bethe lattice Ising model      57 306
Spontaneous magnetization, eight-vertex model      243—244 291 389
Spontaneous magnetization, mean-field Ising model      44
Spontaneous magnetization, planar Ising model      119 299 304— 306 389
Spontaneous magnetization, spherical model      68—69
Spontaneous magnetization, three spin model      319
Spontaneous polarization and spontaneous staggered polarization, eight-vertex model      244—245 253 285
Spontaneous polarization and spontaneous staggered polarization, ice-type model      153—154 157 159
Spontaneous polarization and spontaneous staggered polarization, three-spin model      319
Star-triangle relation, eight-vertex model      210—215 219— 281 289-291
Star-triangle relation, general two-dimensional IRF model      370—374
Star-triangle relation, hard hexagon model      410—411
Star-triangle relation, ice-type model      187—192
Star-triangle relation, operator form      83—85 124 188 192 215 372—373
Star-triangle relation, planar Ising model      80—86 92—93 122-124
Star-triangle relation, three-dimensional      453
susceptibility      4 18
Susceptibility, divergent for the spherical model      70
Thirty-two vertex model      309—313
Three-colourings of the square lattice      165—179
Three-spin model      see triangular three-spin model
Transfer matrix, commutation      see commuting transfer matrices
Transfer matrix, corner      see corner transfer matrices
Transfer matrix, edge      see local transfer matrices
Transfer matrix, eight-vertex model      185 214
Transfer matrix, face      see local transfer matrices
Transfer matrix, general two-dimensional IRF model      371
Transfer matrix, hard hexagon model      452
Transfer matrix, ice-type model      130—131 185
Transfer matrix, one-dimensional Ising model      33—34
Transfer matrix, planar Ising model      85—86 89—96
Transfer matrix, three-colourings of the square lattice      167
Transfer matrix, vertex      see local transfer matrices $U_{i}$
Triangular lattice gas with nearest- neighbour exculsion      see hard hexagon model
Triangular three-spin model      314—321
Twenty-vertex model      311—312
Universality, and violations thereof      7—8 253—255 361-362
van der Waal’s equation of state      13 30—31
Wave numbers, in the Bethe ansatz      143—144 169—170 177
Weak-graph expansion      206
Wiener — Hopf factorization, of eight- vertex model eigenvalue equation      229 231
XYZ chain      258—267 269—272

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