Integrable aspects of the scaling q-state Potts models II: Finite-size effects

Nuclear Physics B

Volumn 661, Issue 3, 2003, Pages 464-513

  Dorey, Patrick ^a   Pocklington, Andrew ^b   Tateo, Roberto ^a  

^a DURHAM UNIVERSITY   (United Kingdom)

^b SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037508537     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(03)00182-2     Document Type: Review

References (94)

1. Potts R.B. Proc. Cambridge Phil. Soc. 48 1952 106
2. Fortuin E.M. Kasteleyn P. On the random-cluster model.1. Introduction and relation to other models Physica 57 1972 536-564
3. Nienhuis B. Berker A.N. Riedel E.K. Schick M. First- and second-order phase transitions in Potts models: renormalization-group solution Phys. Rev. Lett. 43 1979 737
4. Dorey P. Pocklington A. Tateo R. Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure Nucl. Phys. B 661 2003 425-463 preceding article in this issue, hep-th/0208111
5. Chim L. Zamolodchikov A.B. Integrable field theory of q-state Potts model with 0
6. Coleman S. Thun H.J. On the prosaic origin of the double poles in the sine-Gordon S-matrix Commun. Math. Phys. 61 1978 31
7. 12-perturbated minimal models of conformal field theory Int. J. Mod. Phys. A 6 1991 1407-1428
8. Izergin A.G. Korepin V.E. The inverse scattering method approach to the quantum Shabat-Mikhailov model Commun. Math. Phys. 79 1981 303-331
9. Kausch H.G. Takacs G. Watts G.M.T. On the relation between Phi(1,2) and Phi(1,5) perturbed minimal models Nucl. Phys. B 489 1997 557-579 hep-th/9605104
10. Takacs G. Watts G. RSOS revisited Nucl. Phys. B 642 2002 456-482 hep-th/0203073
11. Fendley P. Read N. Exact S-matrices for supersymmetric sigma models and the Potts model hep-th/0207176
12. Dorey P. Tateo R. Nucl. Phys. B 603 2001 582 Erratum hep-th/9910102
13. Zamolodchikov Al.B. Thermodynamics of imaginary coupled sine-Gordon. Dense polymer finite-size scaling function Phys. Lett. B 335 1994 436-454
14. Warnaar S.O. Nienhuis B. Seaton K.A. New construction of solvable lattice models including an Ising model in a field Phys. Rev. Lett. 69 1992 710-712
15. Roche P. On the construction of integrable dilute A-D-E models Phys. Lett. B 285 1992 49-53 hep-th/9204036
16. Warnaar S.O. Pearce P.A. Seaton K.A. Nienhuis B. Order parameters of the dilute A models J. Stat. Phys. 74 1994 466-531 hep-th/9305134
17. 8 structure in the Ising model in a field Nucl. Phys. B 528 1998 683-700
18. Suzuki J. Hidden E-type structures in dilute A models in: Kashiwara M. Miwa T. (Eds.), Physical Combinatorics 2000 217-247 Birkhaeuser Boston Cambridge, MA hep-th/9909104
19. Belavin A.A. Polyakov A.M. Zamolodchikov A.B. Infinite conformal symmetry in two-dimensional quantum field theory Nucl. Phys. B 241 1984 333-380
20. 3 Potts model Nucl. Phys. B 235 1984 54-74
21. Dotsenko V.S. Fateev V.A. Conformal algebra and multipoint correlation functions in two-dimensional statistical models Nucl. Phys. B 240 1984-312
22. den Nijs M.P.M. A relation between the temperature exponents of the eight-vertex and q-state Potts model J. Phys. A 12 1979 1857
23. Nienhuis B. Analytical calculation of two leading exponents of the dilute Potts model J. Phys. A 15 1982 199-213
24. Nienhuis B. Critical behavior of two-dimensional spin models and charge asymmetry in the Coulomb gas J. Stat. Phys. 34 1984 731
25. (1) conformal invariant theories Commun. Math. Phys. 113 1987 1-26
26. di Francesco P. Saleur H. Zuber J.-B. Relations between the Coulomb gas picture and conformal invariance of two-dimensional critical models J. Stat. Phys. 49 1987 57-79
27. Cardy J.L. Operator content of two-dimensional conformally invariant theories Nucl. Phys. B 270 1986 186-204
28. Cardy J. The stress tensor in quenched random systems, Talk presented at Workshop on Statistical Field Theory Como June 2001 cond-mat/0111031
29. Runkel I. T Watts G.M. A non-rational CFT with c=1 as a limit of minimal models JHEP 0109 2001 006 hep-th/0107118
30. Blöte H.W.J. Cardy J.L. Nightingale M.P. Conformal invariance, the central charge, and universal finite-size amplitudes at criticality Phys. Rev. Lett. 56 1986 742-745
31. Affleck I. Universal term in the free energy at a critical point and the conformal anomaly Phys. Rev. Lett. 56 1986 746-748
32. A.B. Zamolodchikov, Integrable field theory from conformal field theory, in: Proceedings of Taniguchi Symposium, Kyoto, 1988
33. Corrigan E. Dorey P.E. Sasaki R. On a generalised bootstrap principle Nucl. Phys. B 408 1993 579 hep-th/9304065
34. 3/5 model and its generalizations Int. J. Mod. Phys. A 11 1996 677-698 hep-th/9411085
35. Ellem R.M. Bazhanov V.V. Thermodynamic Bethe ansatz for the subleading magnetic perturbation of the tricritical Ising model Nucl. Phys. B 512 1998 563 hep-th/9703026
36. Melzer E. Supersymmetric analogs of the Gordon-Andrews identities, and related TBA systems hep-th/9412154
37. Dorey P. Dunning C. Tateo R. New families of flows between two-dimensional conformal field theories Nucl. Phys. B 578 2000 699-727 hep-th/0001185
38. Zamolodchikov Al.B. Thermodynamic Bethe ansatz in relativistic models. Scaling 3-state Potts and Lee-Yang models Nucl. Phys. B 342 1990 695-720
39. 2 perturbed coset theory and generalizations Int. J. Mod. Phys. A 10 1995 1357 hep-th/9405197
40. Klassen T.R. Melzer E. Purely elastic scattering theories and their ultraviolet limits Nucl. Phys. B 338 1990 485-528
41. 2,2n+1 conformal minimal models Phys. Lett. B 266 1991 363-369
42. Ravanini F. Tateo R. Valleriani A. Dynkin TBAs Int. J. Mod. Phys. A 8 1993 1707-1727 hep-th/9207040
43. Kuniba A. Nakanishi T. Spectra in conformal field theories from the Rogers dilogarithm Mod. Phys. Lett. A 7 1992 3487 hep-th/9206034
44. Kuniba A. Nakanishi T. Suzuki J. Functional relations in solvable lattice models I: functional relations and representation theory Int. J. Mod. Phys. A 9 1994 5215-5266 hep-th/9309137
45. Deligne P. La série exceptionelle des groupes de Lie C. R. Acad. Sci. Paris 322 1 1996 321-326
46. Cohen A.M. de Man R. Computational evidence for Deligne's conjecture regarding exceptional groups C. R. Acad. Sci. Paris 322 1 1996 427-432
47. Deligne P. de Man R. La série exceptionelle des groupes de Lie II C. R. Acad. Sci. Paris 323 1 1996 577-582
48. P. Cvitanovic, Classics illustrated: Group Theory, Nordita notes, 1984; Group Theory webbook at http://www.nbi.dk/GroupTheory
49. Macfarlane A.J. Pfeiffer H. Representations of the exceptional and other Lie algebras with integral eigenvalues of the Casimir operator math-ph/0208014
50. Martins M.J. Complex excitations in the thermodynamic Bethe ansatz approach Phys. Rev. Lett. 67 1991 419
51. Fendley P. Excited-state thermodynamics Nucl. Phys. B 374 1992 667-691 hep-th/9109021
52. Zamolodchikov A.B. S-matrix of the Subleading Magnetic Perturbation of the Tricritical Ising Model 1990 Princeton pp. 1195-90
53. Baxter R.J. Hard Hexagons: Exact solution J. Phys. A 13 1980 L61-L70
54. 1,5 of the minimal models M(P,P′) and the trinomial analog of Bailey's lemma Nucl. Phys. B 519 1998 597 hep-th/9712220
55. 2,1 of the M(p,p+1) models of conformal field theory and related polynomial character identities, math-ha/9809066
56. n spin models: Some exact results from the thermodynamic Bethe ansatz Nucl. Phys. B 470 1996 317 hep-th/9601123
57. Fendley P. Sigma models as perturbed conformal field theories Phys. Rev. Lett. 83 1999 4468-4471 hep-th/9906036
58. Takahashi M. Suzuki M. One-dimensional anisotropic Heisenberg model at finite temperatures Prog. Theor. Phys. 48 1972 2187
59. Tateo R. New functional dilogarithm identities and sine-Gordon Y-systems Phys. Lett. B 355 1995 157 hep-th/9505022
60. 1,2-perturbed minimal models: IRF formulation and bootstrap program Int. J. Mod. Phys. A 9 1994 1909 hep-th/9211134
61. Kirillov A.N. Dilogarithm identities Prog. Theor. Phys. Suppl. 118 1995 61 hep-th/9408113
62. Zamolodchikov Al.B. On the thermodynamic Bethe ansatz equations for the reflectionless ADE scattering theories Phys. Lett. B 253 1991 391-394
63. Gliozzi F. Tateo R. Thermodynamic Bethe ansatz and threefold triangulations Int. J. Mod. Phys. A 11 1996 4051 hep-th/9505102
64. Frenkel E. Szenes A. Thermodynamics Bethe ansatz and dilogarithm identities. 1 hep-th/9506215
65. Caracciolo R. Gliozzi F. Tateo R. A topological invariant of RG flows in 2D integrable quantum field theories Int. J. Mod. Phys. B 13 1999 2927 hep-th/9902094
66. Fomin S. Zelevinsky A. Y-systems and generalized associahedra hep-th/0111053
67. Fateev V.A. The exact relations between the coupling constants and the masses of particles for the integrable perturbed conformal field theories Phys. Lett. B 324 1994 45
68. Privman V. Fisher M.E. Finite-size effects at first-order transitions J. Stat. Phys. 33 1983 385
69. Brézin E. Zinn-Justin J. Finite-size effects in phase transitions Nucl. Phys. B 257 1985 867
70. Klümper A. Batchelor M.T. Pearce P.A. Central charges of the 6- and 19-vertex models with twisted boundary conditions J. Phys. A 24 1991 3111-3133
71. Destri C. de Vega H.J. New thermodynamic Bethe ansatz equations without strings Phys. Rev. Lett. 69 1992 2313
72. Warnaar S.O. Batchelor M.T. Nienhuis B. Critical properties of the Izergin-Korepin and solvable O(n) models and their related quantum spin chains J. Phys. A 25 1992 3077-3095
73. Zamolodchikov A.B. Renormalization group and perturbation theory near fixed points in two-dimensional field theory Sov. J. Nucl. Phys. 46 1987 1090 Yad. Fiz. 46 1987 1819
74. Ludwig A.W. Cardy J.L. Perturbative evaluation of the conformal anomaly at new critical points with applications to random systems Nucl. Phys. B 285 1987 687
75. Zamolodchikov A.B. From tricritical Ising to critical Ising by thermodynamic Bethe ansatz Nucl. Phys. B 358 1991 524
76. Fendley P. Saleur H. Zamolodchikov A.B. Massless flows. 1. The sine-Gordon and O(n) models Int. J. Mod. Phys. A 8 1993 5717 hep-th/9304050
77. Fendley P. Saleur H. Zamolodchikov A.B. Massless flows, 2. The exact S-matrix approach Int. J. Mod. Phys. A 8 1993 5751 hep-th/9304051
78. Dorey P. Nucl. Phys. B 374 1992 741-762 hep-th/9110058
79. Hollowood T.J. Quantizing SL(N) solitons and the Hecke algebra Int. J. Mod. Phys. A 8 1993 947-982
80. (1) affine Toda solitons Nucl. Phys. B 449 1995 375-405 hep-th/9501136
81. Saleur H. Wehefritz-Kaufmann B. Thermodynamics of the complex SU(3) Toda theory Phys. Lett. B 481 2000 419-426 hep-th/0003217
82. Bazhanov V. Reshetikhin N.Yu. Restricted solid on solid models connected with simply laced algebras and conformal field theory J. Phys. A 23 1990 1477
83. Jûttner G. Klûmper A. Suzuki J. From fusion hierarchy to excited state TBA Nucl. Phys. B 512 1998 581-600
84. Kuniba A. Sakai K. Suzuki J. Continued fraction TBA and functional relations in XXZ model at root of unity Nucl. Phys. B 525 1998 597-626
85. Bazhanov V.V. Lukyanov S.L. Zamolodchikov A.B. Integrable quantum field theories in finite volume: Excited state energies Nucl. Phys. B 489 1997 487-531 hep-th/9607099
86. Dorey P. Tateo R. Excited states by analytic continuation of TBA equations Nucl. Phys. B 482 1996 639-659 hep-th/9607167
87. Dorey P. Tateo R. Excited states in some simple perturbed conformal field theories Nucl. Phys. B 515 1998 575-623 hep-th/9706140
88. Fioravanti D. Mariottini A. Quattrini E. Ravanini F. Excited state Destri-De Vega equation for sine-Gordon and restricted sine-Gordon models Phys. Lett. B 390 1997 243-251 hep-th/9608091
89. 3,5 model hep-th/0205238
90. Bazhanov V. Lukyanov S. Zamolodchikov A.B. Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz Commun. Math. Phys. 177 1996 381-398 hep-th/9412229
91. 3 conformal field theory, quantum boussinesq theory and boundary affine Toda theory Nucl. Phys. B 622 2002 475-547 hep-th/0105177
92. Fioravanti D. Ravanini F. Stanishkov M. Generalized KdV and quantum inverse scattering description of conformal minimal models Phys. Lett. B 367 1996 113-120 hep-th/9510047
93. Fioravanti D. Rossi M. A braided Yang-Baxter algebra in a theory of two coupled lattice quantum KdV: algebraic properties and ABA representations J. Phys. A 35 2002 3647-3682 hep-th/0104002
94. Braden H.W. Corrigan E. Dorey P.E. Sasaki R. Affine Toda field theory and exact S-matrices Nucl. Phys. B 338 1990 689-746