English

Dimer statistics on the M\"obius strip and the Klein bottle

Statistical Mechanics 2009-10-31 v2 Combinatorics

Abstract

Closed-form expressions are obtained for the generating function of close-packed dimers on a 2M×2N2M \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.

Keywords

Cite

@article{arxiv.cond-mat/9906154,
  title  = {Dimer statistics on the M\"obius strip and the Klein bottle},
  author = {W. T. Lu and F. Y. Wu},
  journal= {arXiv preprint arXiv:cond-mat/9906154},
  year   = {2009}
}

Comments

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