Dimer problem on the cylinder and torus
نویسندگان
چکیده
Weobtain explicit expressions of the number of close-packed dimers and entropy for three types of lattices (the so-called 8.8.6, 8.8.4, andhexagonal lattices)with cylindrical boundary condition and the entropy of the 8.8.6 lattice with toroidal boundary condition. Our results and the one on 8.8.4 and hexagonal lattices with toroidal boundary condition by Salinas and Nagle [S.R. Salinas, J.F. Nagle, Theory of the phase transition in the layered hydrogenbonded SnCl·2H2O crystal, Phys. Rev. B 9 (1974) 4920–4931] and Wu [F.Y. Wu, Dimers on two-dimensional lattices, Inter. J. Modern Phys. B 20 (2006) 5357–5371] imply that the 8.8.6 (or 8.8.4) lattices with cylindrical and toroidal boundary conditions have the same entropy whereas the hexagonal lattices have not. Based on these facts we propose the following problem: under which conditions do the lattices with cylindrical and toroidal boundary conditions have the same entropy? © 2008 Elsevier B.V. All rights reserved.
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