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Dimer problem for some three dimensional lattice graphs

Author

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  • Lin, Fenggen
  • Chen, Ailian
  • Lai, Jiangzhou

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.

Suggested Citation

  • Lin, Fenggen & Chen, Ailian & Lai, Jiangzhou, 2016. "Dimer problem for some three dimensional lattice graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 347-354.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:347-354
    DOI: 10.1016/j.physa.2015.09.027
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    References listed on IDEAS

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    1. Yan, Weigen & Yeh, Yeong-Nan & Zhang, Fuji, 2008. "Dimer problem on the cylinder and torus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(24), pages 6069-6078.
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