Portal de Periódicos da CAPES

Dimer statistics on the Möbius strip and the Klein bottle

1999; Elsevier BV; Volume: 259; Issue: 2 Linguagem: Inglês

10.1016/s0375-9601(99)00420-x

1873-2429

Wentao Lu, F Y Wu,

Advanced Mathematical Theories and Applications

Closed-form expressions are obtained for the generating function of close-packed dimers on a 2M×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.