The emerging role of number theory in exactly solvable models in lattice statistical mechanics
Tài liệu tham khảo
Akutsu, 1986, Exactly solvable IRF models. II. SN-generalizations, J. Phys. Soc. Jpn., 55, 1466, 10.1143/JPSJ.55.1466
Akutsu, 1986, Exactly solvable IRF models. III. A new hierarchy of solvable models, J. Phys. Soc. Jpn., 55, 1880, 10.1143/JPSJ.55.1880
Alder, 1969, Partition identities-from Euler to the present, Amer. Math. Monthly, 76, 733, 10.2307/2317861
Andrews, 1976
Andrews, 1981, The hard-hexagon model and Rogers-Ramanujan type identities, 78, 5290
Andrews, 1984, Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities, J. Stat. Phys., 35, 193, 10.1007/BF01014383
Andrews, 1986, Lattice gas generalization of the hard hexagon model: II. The local densities as elliptic functions, J. Stat. Phys., 44, 713, 10.1007/BF01011904
Babelon, 1982, Exact solution of the Zn+1 × Zn+1 symmetric generalization of the XXZ model, Nucl. Phys. B, 200, 266, 10.1016/0550-3213(82)90087-6
Barber, 1973, On the spontaneous order of the eight-vertex model, J. Phys. C., 6, 2913, 10.1088/0022-3719/6/20/004
Bazhanov, 1982, Trigonometric and Sn symmetric solutions of triangle equations with variables on the faces, Nucl. Phys. B, 205, 505, 10.1016/0550-3213(82)90075-X
Bazhanov, 1984, Free fermions on a three dimensional lattice and tetrahedron equations, Nucl. Phys. B, 230, 435, 10.1016/0550-3213(84)90103-2
Baxter, 1972, Partition function of the eight-vertex lattice model, Ann. of Phys., 70, 193, 10.1016/0003-4916(72)90335-1
Baxter, 1973, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg Chain. I. Some fundamental eigenvectors, Ann. of Phys., 76, 1, 10.1016/0003-4916(73)90439-9
Baxter, 1973, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain. II. Equivalence to a generalized ice-type lattice model, Ann. of Phys., 76, 25, 10.1016/0003-4916(73)90440-5
Baxter, 1973, Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg Chain. III. Eigenvectors of the transfer matrix and Hamiltonian, Ann. of Phys., 76, 48, 10.1016/0003-4916(73)90441-7
Baxter, 1976, Corner transfer matrices of the eight-vertex model. I. Low-temperature expansions and conjectured properties, J. Stat. Phys., 15, 485, 10.1007/BF01020802
Baxter, 1977, Corner transfer matrices of the eight-vertex model. II. The Ising model case, J. Stat. Phys., 17, 1, 10.1007/BF01089373
Baxter, 1980, Hard hexagons: Exact solution, J. Phys. A: Math. Gen., 13, L61, 10.1088/0305-4470/13/3/007
Baxter, 1981, Corner transfer matrices, Physica, 106A, 18, 10.1016/0378-4371(81)90203-X
Baxter, 1981, Rogers-Ramanujan identities in the hard hexagon model, J. Stat. Phys., 26, 427, 10.1007/BF01011427
Baxter, 1982
Baxter, 1982, The inversion relation method for some two-dimensional exactly solved models in lattice statistics, J. Stat. Phys., 28, 1, 10.1007/BF01011621
Baxter, 1983, On Zamolodchikov's solution of the tetrahedron equations, Commun. Math. Phys., 88, 185, 10.1007/BF01209476
Baxter, 1985, Exactly solved models in statistical mechanics
Baxter, 1986, The Yang-Baxter equations and the Zamolodchikov model, Physica, 18D, 321
Baxter, 1986, Lattice gas generalization of the hard hexagon model: I. Star-triangle relation and local densities, J. Stat. Phys., 44, 249, 10.1007/BF01010916
Baxter, 1982, Hard hexagons: Interfacial tension and correlation length, J. Phys. A, 15, 897, 10.1088/0305-4470/15/3/027
Baxter, 1983, Hard squares with diagonal attractions, J. Phys. A., 16, 2239, 10.1088/0305-4470/16/10/022
Belavin, 1981, Dynamical symmetry of integrable quantum systems, Nucl. Phys. B, 180, 189, 10.1016/0550-3213(81)90414-4
Belavin, 1984, Triangle equations and simple Lie algebras, Vol. 4, 93
Belavin, 1984, Infinite conformal symmetry in two-dimensional quantum theory, Nucl. Phys. B, 241, 333, 10.1016/0550-3213(84)90052-X
Belavin, 1982, The partition function of the Zn×Zn invariant vertex lattice model, Phys. Lett. B, 116, 165, 10.1016/0370-2693(82)91000-0
Birch, 1975, A look back at Ramanujan's notebooks, 78, 73
Bovier, 1983, Factorized S matrices and generalized Baxter models, J. Math. Phys., 24, 631, 10.1063/1.525709
Bressoud, 1980, Analytic and combinatorial generalizations of the Rogers-Ramanujan identities
Cherednik, 1982, On the properties of factorized S matrices in elliptic functions, Sov. J. Nucl. Phys., 36, 320
Chudnovsky, 1981, Completely X-symmetric S-matrices corresponding to theta functions, Phys. Lett. A, 81, 105, 10.1016/0375-9601(81)90034-7
Creamer, 1980, Gelfand-Levitan method for operator fields, Phys. Rev. D, 21, 1523, 10.1103/PhysRevD.21.1523
1981, J. Math. Phys., 22, 1084, 10.1063/1.524991
Fateev, 1985, Parafermionic currents in the two-dimensional conformal field theory and self-dual critical points in Zn-invariant statistical systems, L.D. Landau Institute preprint
Forrester, 1985, Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities, J. Stat. Phys., 38, 435, 10.1007/BF01010471
Huse, 1984, Exact exponents for infinitely many new multi-critical points, Phys. Rev. B, 30, 3908, 10.1103/PhysRevB.30.3908
Hua, 1982
Jimbo, 1984, Some remarks on the differential approach to the star-triangle relation, Lett. Math. Phys., 8, 529, 10.1007/BF00400983
Jimbo, 1985, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys., 10, 63, 10.1007/BF00704588
Jimbo, 1985, A solvable lattice model and related Rogers-Ramanujan type identities, Physica, 15D, 335
Jimbo, 1985, Classification of solutions to the star-triangle relation for a class of 3- and 4-state IRF models, Nucl. Phys. B, 257, 1, 10.1016/0550-3213(85)90332-3
M. Jimbo, T. Miwa and M. Okado, Solvable lattice models with broken ZN symmetry and Hecke's indefinite modular forms, RIMS-536 preprint.
V.G. Kac and D.H. Peterson, Infinite-dimensional Lie algebras, theta functions, and modular forms, Adv. in Math. 53 (198) 125–264.
Kasteleyn, 1975, Exactly solvable lattice models, vol. 3
Kolberg, 1957, Some identities involving the partition function, Math. Scand., 5, 77, 10.7146/math.scand.a-10492
Knopp, 1970
Kulish, 1982, Quantum spectral transform method. Recent developments, Lect. Notes in Physics, 151, 61, 10.1007/3-540-11190-5_8
Kulish, 1982, Solutions of the Yang-Baxter equation, J. Soviet Math., 19, 1596, 10.1007/BF01091463
Kulish, 1981, Yang-Baxter equation and representation theory I, Lett. Math. Phys., 5, 393, 10.1007/BF02285311
Kuniba, 1986, Exactly solvable IRF models. I. A three-state model, J. Phys. Soc. Jpn., 55, 1092, 10.1143/JPSJ.55.1092
A. Kuniba, Y. Akutsu and M. Wadati, Exactly solvable IRF models. IV. Generalized Rogers-Ramanujan identities and a solvable hierarchy, preprint.
A. Kuniba, Y. Akutsu and M. Wadati, The Gordon-generalization hierarchy of exactly solvable IRF models, preprint.
Lang, 1976
Lepowsky, 1982, A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities, Adv. in Math., 45, 21, 10.1016/S0001-8708(82)80012-1
Lieb, 1967, Residual entropy of square ice, Phys. Rev., 162, 162, 10.1103/PhysRev.162.162
Lieb, 1967, Exact solution of the F model of an antiferroelectric, Phys. Rev. Lett., 18, 1046, 10.1103/PhysRevLett.18.1046
Lieb, 1967, Exact solution of the two-dimensional Slater KDP model of a ferroelectric, Phys. Rev. Lett., 19, 108, 10.1103/PhysRevLett.19.108
Lieb, 1972, vol. 1, 321
Montroll, 1963, Correlations and spontaneous magnetization of the two-dimensional Ising model, J. Math. Phys., 4, 308, 10.1063/1.1703955
Mumford, 1983
Onsager, 1944, Crystal Statistics, I. A two-dimensional model with an order-disorder transition, Phys. Rev., 65, 117, 10.1103/PhysRev.65.117
Onsager, 1949, Nuovo Cimento Suppl., 6, 261, 10.1007/BF02780991
Ottinger, 1982, Note on the Yang-Baxter equations for generalized Baxter models, Phys. Lett. A, 88, 339, 10.1016/0375-9601(82)90609-0
Palmer, 1981, Two-dimensional Ising correlations: Convergence of the scaling limit, Adv. in Applied Math., 2, 329, 10.1016/0196-8858(81)90010-5
Pearce, 1983, Thermodynamic models with exact solutions, Sci. Prog. Oxf., 68, 189
Pearce, 1985, Magnetic hard squares: Exact solution, J. Phys. A, 18, 3217, 10.1088/0305-4470/18/16/022
Pearce, 1984, Deviations from critical density in the generalized hard hexagon model, J. Phys. A, 17, 2095, 10.1088/0305-4470/17/10/021
Perk, 1980, New families of commuting transfer matrices in q-state vertex models, Phys. Lett. A, 84, 407, 10.1016/0375-9601(81)90994-4
Perk, 1982, Families of commuting transfer matrices in q-state vertex models
Perk, 1986, Nonintersecting string model and graphical approach: Equivalence with a Potts model, J. Stat. Phys., 42, 727, 10.1007/BF01010443
Perk, 1986, Graphical approach to the nonintersecting string model: Star-triangle equation, inversion relation, and exact solution, Physica, 138A, 100, 10.1016/0378-4371(86)90175-5
Rademacher, 1974, The Ramanujan identities under modular substitutions, vol. II
Richey, 1986, Zn Baxter model: Symmetries and the Belavin parametrization, J. Stat Phys., 42, 311, 10.1007/BF01127715
Schoeneberg, 1974
Schultz, 1981, Solvable q-state models in lattice statistics and quantum field theory, Phys. Rev. Lett., 46, 629, 10.1103/PhysRevLett.46.629
Schultz, 1983, Eigenvectors of the multi-component generalization of the six-vertex model, Physica, 122A, 71, 10.1016/0378-4371(83)90083-3
Sklyanin, 1983, Some algebraic structures connected with the Yang-Baxter equation, Functional Analy. and Its Applications, 16, 263, 10.1007/BF01077848
Slater, 1951, Further identities of the Rogers-Ramanujan type, 54, 147
Sutherland, 1967, Exact solution of a two-dimensional model for hydrogen-bounded crystals, Phys. Rev. Lett., 19, 103, 10.1103/PhysRevLett.19.103
Sutherland, 1967, Exact solution of a model of two-dimensional ferroelectrics in an arbitrary external field, Phys. Rev. Lett., 19, 588, 10.1103/PhysRevLett.19.588
Sutherland, 1968, Further results for the many-body problem in one dimension, Phys. Rev. Lett., 20, 98, 10.1103/PhysRevLett.20.98
Takhtadzhan, 1983, Quantum inverse scattering method and algebraized matrix Bethe-ansatz, J. Sov. Math., 23, 2470, 10.1007/BF01084176
Takhtadzhan, 1979, The quantum method of the inverse problem and the Heisenberg XYZ model, Russian Math. Surveys, 34, 11, 10.1070/RM1979v034n05ABEH003909
Thacker, 1979, Inverse scattering transform as an operator method in quantum field theory, Phys. Rev. D, 19, 3660, 10.1103/PhysRevD.19.3660
Thacker, 1981, Exact integrability in quantum field theory and statistical systems, Rev. Mod. Phys., 53, 253, 10.1103/RevModPhys.53.253
Thacker, 1986, Corner transfer matrices and Lorentz invariance on a lattice, Physica, 18D, 348
Tracy, 1985, Complete integrability in statistical mechanics and the Yang-Baxter equations, Physica, 14D, 253
Tracy, 1985, Embedded elliptic curves and the Yang-Baxter equations, Physica, 16D, 203
Tracy, 1986, Zn Baxter model: Critical behavior, J. Stat. Phys., 44, 183, 10.1007/BF01010910
C.A. Tracy, L. Grove and M. Newman, Modular properties of the hard hexagon model, preprint.
Wilson, 1983, The renormalization group and critical phenomena, Rev. Mod. Phys., 55, 583, 10.1103/RevModPhys.55.583
Yang, 1952, The spontaneous magnetization of a two-dimensional Ising model, Phys. Rev., 85, 808, 10.1103/PhysRev.85.808
Yang, 1967, Some exact results for the many-body problem in one dimension with repulsive delta function interaction, Phys. Rev. Lett., 19, 1312, 10.1103/PhysRevLett.19.1312
Yang, 1966, One-dimensional chain of anisotropic spin-spin interactions. I. proof of Bethe's hypothesis for ground state in a finite system, Phys. Rev., 150, 321, 10.1103/PhysRev.150.321
Yang, 1966, One-dimensional chain of anisotropic spin-spin interactions. II. Properties of the ground state energy per lattice site for an infinite system, Phys. Rev., 150, 327, 10.1103/PhysRev.150.327
Yang, 1966, One-dimensional chain of anisotropic spin-spin interactions. III. Applications, Phys. Rev., 151, 258, 10.1103/PhysRev.151.258
Zamolodchikov, 1980, Factorized S matrices and lattice statistical systems, vol. 2, 1
Zamolodchikov, 1981, Tetrahedron equations and the relativistic S-matrix of straight-strings in 2+1-dimensions, Commun. Math. Phys., 79, 489, 10.1007/BF01209309
