Dimer problem on the cylinder and torus

Weigen Yan, Yeong-Nan Yeh and Fuji Zhang

Physica A: Statistical Mechanics and its Applications, 2008, vol. 387, issue 24, 6069-6078

Abstract: We obtain 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, and hexagonal 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 hydrogen-bonded SnCl2⋅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?

Keywords: Dimer problem; 8.8.4 lattice; 8.8.6 lattice; Hexagonal lattice; Cylindrical and toroidal boundary conditions (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:387:y:2008:i:24:p:6069-6078

DOI: 10.1016/j.physa.2008.06.042

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