Dimer statistics on the Möbius strip and the Klein bottle

Abstract

Closed-form expressions are obtained for the generating function of close-packed dimers on a $2M\times 2N$ simple quartic lattice embedded on a Möbius 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 Möbius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Möbius strips and cylinders.

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

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