Dimer statistics on the Möbius strip and the Klein bottle

Details Dimer statistics on the Möbius strip and the Klein bottle Dimer statistics on the Möbius strip and the Klein bottle

1999-06-10

arxiv.org/abs/cond-mat/9906154v2

Physics Letters A 259,108-114(1999)

Physics

Condensed Matter

Statistical Mechanics

12 pages, 2 figs included, accepted by Phys. Lett. A

Scientific paper

10.1016/S0375-9601(99)00420-X

Closed-form expressions are obtained for the generating function of close-packed dimers on a $2M \times 2N$ simple quartic lattice embedded on a M\"obius strip and a Klein bottle. Finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices of the same size and with a square symmetry, the number of dimer configurations on a M\"obius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for M\"obius strips and cylinders.

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