Close-packed dimers on nonorientable surfaces

Abstract

The problem of enumerating dimers on an M x N net embedded on non-orientable surfaces is considered. We solve both the Moebius strip and Klein bottle problems for all M and N with the aid of imaginary dimer weights. The use of imaginary weights simplifies the analysis, and as a result we obtain new compact solutions in the form of double products. The compact expressions also permit us to establish a general reciprocity theorem.

13 pages, 1 figure, typo corrected to the version published in Phys. Lett. A 293, 235 (2002)

References in corpus (1)

• Finite-size scaling for the Ising model on the Moebius strip and the Klein bottle

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