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



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Ќазвание: Exactly Solved Models in Statistical Mechanics

јвтор: Baxter R.J.

јннотаци€:

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: en

–убрика: ћеханика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1982

 оличество страниц: 486

ƒобавлена в каталог: 16.04.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$Z_{N}$ model      322
Anti-ferroelectric phase of eight-vertex model      246
Anti-ferroelectric phase of ice-type model      152
Ashkin Ч Teller model      254 353Ч362
Asymptotic degeneracy of maximum, eigenvalues of the transfer matrix      111Ч114 152Ч153 239Ч 240
Bethe ansatz      139 168
Bethe lattice      13 47Ч59 306Ч309 351
Cayley tree      47Ч49
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      370Ч372
Commuting transfer matrices, hard hexagon model      452
Commuting transfer matrices, ice-type model      180Ч181 185Ч186
Commuting transfer matrices, planar Ising model      85Ч86 96
Corner transfer matrices      363Ч401
Corner transfer matrices, eight-vertex model      385Ч389
Corner transfer matrices, hard hexagon model      405Ч407 426Ч 432
correlation length      19
Correlation length, eight-vertex model      241Ч243 284
Correlation length, hard hexagon model      452
Correlation length, ice-type model      154Ч155
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 115Ч118
Correlations      10 18Ч19
Correlations, one-dimensional Ising model      35Ч36
Correlations, planar Ising model      297Ч298
Critical exponents      4 17 19 20 29
Critical exponents, Ashkin Ч Teller model      360Ч361
Critical exponents, Bethe lattice Ising model      58
Critical exponents, classical values      30Ч31
Critical exponents, continuously variable      8 253Ч254 361
Critical exponents, eight-vertex model      253Ч255
Critical exponents, hard hexagon model      448Ч452
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      351Ч352
Critical exponents, spherical model      69Ч71
Critical exponents, three-spin model      320Ч321
Critical point      3 10 28
Critical point, Ashkin Ч Teller model      359Ч362
Critical point, Bethe lattice Ising model      54 307Ч 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      77Ч78 87 120Ч121 307Ч308
Critical point, Potts model      338Ч339 347Ч348
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      124Ч126
Disorder points      247
Dual lattice      74 79
Duality, Ashkin Ч Teller model      357
Duality, eight-vertex model      206
Duality, planar Ising model      73Ч80 86Ч87
Duality, Potts model      338 346
Eight-vertex model      202Ч321
Eight-vertex model, СelectricТ arrow formulation      202Ч 204 276Ч279
Eight-vertex model, СmagneticТ spin formulation      207Ч 210 286Ч289
Elliptic functions      455Ч473
Elliptic functions, conjugate modulus identities      419 444 446 467Ч468
Elliptic functions, in eight-vertex model      212Ч215
Elliptic functions, in hard hexagon model      412Ч415
Elliptic functions, in planar Ising model      102Ч103
Elliptic functions, in square-lattice four-colouring problem      171Ч176
F model      129
Ferroelectric ice-type model in a field      160Ч165
Ferroelectric phase of eight-vertex model      246
Ferroelectric phase of ice-type model      151
Four colour problem      331Ч332
Free energy      16Ч17
Free energy, Bethe lattice Ising model      55Ч56 59 306
Free energy, critical Potts model      339Ч340 348- 350
Free energy, eight-vertex model      236Ч237 285Ч 286
Free energy, hard hexagon model      408 426 444 450
Free energy, ice-type model      145Ч150
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      110Ч111 296Ч 306
Free energy, spherical model      61Ч64
Free energy, three-spin model      319Ч320
Free-fermion model      270Ч271 310
Hard hexagon model      402Ч454
Heisenberg chain      see XYZ chain
Hyperbolic trigonometry and the star- triangle relation      292
Hyperscaling      7
Ice model      127Ч129 148
Ice-type model      127Ч201
Interfacial tension      20 110Ч114 152 153 239Ч241 452
Internal energy      9 16
Internal energy, critical Potts model      344Ч345 349Ч 351
Internal energy, spherical model      64
Inversion relations for local transfer matrices, free energy, and corner transfer matrices      383Ч 387 421Ч423 427-429
Ising model      19Ч32 (see also specific properties e.g.
Ising model, Bethe lattice      13 47Ч59 306Ч309
Ising model, mean field      13 39Ч46
Ising model, one-dimensional      12 32Ч38
Ising model, planar      72Ч126 294Ч309
Ising model, relation of d-dimensional model to a (d-1)-dimensional quantum- mechanical model      266Ч267
Kagom$\acute{e}$ lattice      276Ч277
KDP model      129
Landen transformation      466Ч467
Latent heat of Potts model      345 349Ч351
Lattice gas      24Ч30
Lattice gas, hard hexagons      402 409
Lattice gas, mean field      46
LiouvilleТs theorem      458
Local transfer matrices $U_{i}$, edge transfer matrices for the planar Ising model      84Ч85 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      1Ч4 17 21Ч23
Magnetization, Bethe lattice Ising model      52Ч54 59
Magnetization, mean-field Ising model      41
Magnetization, one dimensional Ising model      34
Magnetization, spherical model      64
Mean-field model      13 39Ч46
Medial graph      325 332Ч333 345Ч346
One-dimensional Ising model      12 32Ч38
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      8Ч9 16 25
Partition function, per site      see free energy
Percolation problem      324
Pfaffian      125
Phase transition      1Ч3 (see also critical point)
Poisson summation formula      468Ч469
Polarization      see also spontaneous polarization
Polarization, ferroelectric ice-type model      162Ч165
Potts model      322Ч352
Renormalization group      11
Rogers Ч Ramanujan and related identities      434Ч443
Scaling hypothesis      4Ч7 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 22Ч23 395Ч396 404
Six-vertex model      see ice-type model
Specific heat      16
Spherical model      13 60Ч71
Spontaneous magnetization      1Ч4 23
Spontaneous magnetization, Bethe lattice Ising model      57 306
Spontaneous magnetization, eight-vertex model      243Ч244 291 389
Spontaneous magnetization, mean-field Ising model      44
Spontaneous magnetization, planar Ising model      119 299 304Ч 306 389
Spontaneous magnetization, spherical model      68Ч69
Spontaneous magnetization, three spin model      319
Spontaneous polarization and spontaneous staggered polarization, eight-vertex model      244Ч245 253 285
Spontaneous polarization and spontaneous staggered polarization, ice-type model      153Ч154 157 159
Spontaneous polarization and spontaneous staggered polarization, three-spin model      319
Star-triangle relation, eight-vertex model      210Ч215 219Ч 281 289-291
Star-triangle relation, general two-dimensional IRF model      370Ч374
Star-triangle relation, hard hexagon model      410Ч411
Star-triangle relation, ice-type model      187Ч192
Star-triangle relation, operator form      83Ч85 124 188 192 215 372Ч373
Star-triangle relation, planar Ising model      80Ч86 92Ч93 122-124
Star-triangle relation, three-dimensional      453
susceptibility      4 18
Susceptibility, divergent for the spherical model      70
Thirty-two vertex model      309Ч313
Three-colourings of the square lattice      165Ч179
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      130Ч131 185
Transfer matrix, one-dimensional Ising model      33Ч34
Transfer matrix, planar Ising model      85Ч86 89Ч96
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      314Ч321
Twenty-vertex model      311Ч312
Universality, and violations thereof      7Ч8 253Ч255 361-362
van der WaalТs equation of state      13 30Ч31
Wave numbers, in the Bethe ansatz      143Ч144 169Ч170 177
Weak-graph expansion      206
Wiener Ч Hopf factorization, of eight- vertex model eigenvalue equation      229 231
XYZ chain      258Ч267 269Ч272
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