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 2 M ×2 N simple quartic lattice embedded on a Mobius 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 Mobius strip is 70.2% of that on a cylinder. We also establish two identities relating dimer generating functions for Mobius strips and cylinders.