Dimer problem on the cylinder and torus
Tài liệu tham khảo
Allen, 1974, Dimer models for the antiferroelectric transition in copper formate tetrahydrate, J. Chem. Phys., 60, 3299, 10.1063/1.1681521
Ciucu, 1997, Enumeration of perfect matchings in graphs with reflective symmetry, J. Combin. Theory Ser. A, 77, 67, 10.1006/jcta.1996.2725
Cohn, 1996, Local statistics for random domino tilings of the Aztec diamond, Duke Math. J., 85, 117, 10.1215/S0012-7094-96-08506-3
Cohn, 2001, A variational principle for domino tilings, J. Amer. Math. Soc., 14, 297, 10.1090/S0894-0347-00-00355-6
Davis, 1979
Elkies, 1992, Alternating sign matrices and domino tilings, J. Alg. Combin., 1, 111, 10.1023/A:1022420103267
Elser, 1984, Solution of the dimer problem on a hexagonal lattice with boundary, J. Phys. A, 17, 1509, 10.1088/0305-4470/17/7/018
Fisher, 1961, Statistical mechanics of dimers on a plane lattice, Phys. Rev., 124, 1664, 10.1103/PhysRev.124.1664
Fisher, 1970, Asymptotic free energy of a system with periodic boundary conditions, Commun. Math. Phys., 19, 251, 10.1007/BF01646633
Gutman, 1988
Izmailian, 2003, Exact finite-size corrections of the free energy for the square lattice dimer model under different boundary conditions, Phys. Rev. E, 67, 066114, 10.1103/PhysRevE.67.066114
Izmailian, 2006, Finite-size corrections and scaling for the triangular lattice dimer model with periodic boundary conditions, Phys. Rev. E, 73, 016128, 10.1103/PhysRevE.73.016128
Izmailian, 2005, Logarithmic conformal field theory and boundary effects in the Dimer model, Phys. Rev. Lett., 95, 260602, 10.1103/PhysRevLett.95.260602
Kasteleyn, 1961, The statistics of dimers on a lattice I: The number of dimer arrangements on a quadratic lattice, Physica, 27, 1209, 10.1016/0031-8914(61)90063-5
Kasteleyn, 1963, Dimer statistics and phase transitions, J. Math. Phys., 4, 287, 10.1063/1.1703953
Kasteleyn, 1967, Graph theory and crystal physics, 43
Kenyon, 2006, Dimers and amoebae, Ann. Math., 163, 1019, 10.4007/annals.2006.163.1019
Korepin, 2000, Thermodynamic limit of the six-vertex model with domain wall boundary conditions, J. Phys. A, 33, 7053, 10.1088/0305-4470/33/40/304
Kuo, 2004, Applications of graphical condensation for enumerating matchings and tilings, Theoret. Comput. Sci., 319, 29, 10.1016/j.tcs.2004.02.022
Little, 1975, A characterization of convertible (0, 1)-matrices, J. Combin. Theory Ser. B, 18, 187, 10.1016/0095-8956(75)90048-9
Lovász, 1986
Lu, 1998, Physica A, 258, 157, 10.1016/S0378-4371(98)00273-8
Lu, 1999, Dimer statistics on the Mobius strip and the Klein bottle, Phys. Lett. A, 259, 108, 10.1016/S0375-9601(99)00420-X
McCuaig, 2004, Polyá’s permanent problem, Electron. J. Combin., 11, R79, 10.37236/1832
W. McCuaig, N. Robertson, P.D. Seymour, R. Thomas, Permanents, Pfaffian orientations, and even directed circuits (Extended abstract), in: Proc. Symp. on the Theory of Computing, STOC’97, 1997
McCoy, 1973
Nagle, 1989, Dimer models on anisotropic lattices, vol. 13
Propp, 2003, Generalized domino-shuffling, Theoret. Comput. Sci., 303, 267, 10.1016/S0304-3975(02)00815-0
Propp, 1999, Enumerations of matchings: Problems and progress, vol. 38, 255
Robertson, 1999, Permanents, Pfaffian orientations, and even directed circuits, Ann. Math., 150, 929, 10.2307/121059
Sachs, 1994, Remark on the dimer problem, Discrete Appl. Math., 51, 171, 10.1016/0166-218X(94)90106-6
Salinas, 1974, Theory of the phase transition in the layered hydrogen-bonded SnCl2⋅2H2O crystal, Phys. Rev. B, 9, 4920, 10.1103/PhysRevB.9.4920
Stembridge, 1990, Nonintersecting paths, pfaffians, and plane partitions, Adv. Math., 38, 96, 10.1016/0001-8708(90)90070-4
Temperley, 1961, Dimer problem in statistical mechanics—An exact result, Philos. Magazine, 6, 1061, 10.1080/14786436108243366
Thomas, 2006
Wu, 2008, Dimers on the kagome lattice I: Finite lattices, Physica A, 387, 4148, 10.1016/j.physa.2008.02.054
Wu, 2006, Dimers on two-dimensional lattices, Internat. J. Modern Phys. B, 20, 5357, 10.1142/S0217979206036478
Wu, 1967, Exactly soluble model of the ferroelectric phase transition in two dimensions, Phys. Rev. Lett., 18, 605, 10.1103/PhysRevLett.18.605
Wu, 1968, Remarks on the modified potassium dihydrogen phosphate model of a ferroelectric, Phys. Rev., 168, 539, 10.1103/PhysRev.168.539
Wu, 1989, Critical frontier of the antiferromagnetic Ising model in a magnetic field: The honeycomb lattice, Phys. Rev. Lett., 62, 2773, 10.1103/PhysRevLett.62.2773
Yan, 2004, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math., 32, 655, 10.1016/S0196-8858(03)00097-6
Yan, 2005, Graphical condensation for enumerating perfect matchings, J. Combin. Theory Ser. A, 110, 113, 10.1016/j.jcta.2004.10.005
Yan, 2006, Enumeration of perfect matchings of a type of Cartesian products of graphs, Disrete Appl. Math., 154, 145, 10.1016/j.dam.2005.07.001