Dimer statistics of honeycomb lattices on Klein bottle, Möbius strip and cylinder

Wei Li and Heping Zhang

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 15, 3833-3848

Abstract: Dimer statistics is a central problem in statistical physics. In this paper the enumerations of close-packed dimers of honeycomb lattices on Klein bottle, Möbius strip and cylinder are considered. By establishing a Pfaffian orientation or a crossing orientation, and then computing the determinants of the skew-symmetric matrices of the resulting orientation graphs, we obtain explicit expressions of the number of close-packed dimers of the Klein-bottle polyhex, the Möbius polyhex and the cylindrical polyhex.

Keywords: Close-packed dimers; Honeycomb lattice; Pfaffian orientation; Crossing orientation (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:15:p:3833-3848

DOI: 10.1016/j.physa.2012.03.004

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