Dimer problem for some three dimensional lattice graphs

Fenggen Lin, Ailian Chen and Jiangzhou Lai

Physica A: Statistical Mechanics and its Applications, 2016, vol. 443, issue C, 347-354

Abstract: Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K2×C4×Pn))≈(−1.171⋅n−1.1223+3.146)n, and log(M(K2×P4×Pn))≈(−1.164⋅n−1.196+2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy.

Keywords: Dimer; Entropy; Three dimensional lattice (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:443:y:2016:i:c:p:347-354

DOI: 10.1016/j.physa.2015.09.027

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