Close-packed dimers on nonorientable surfaces
Statistical Mechanics
2009-11-07 v3 Mathematical Physics
Combinatorics
math.MP
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.
Cite
@article{arxiv.cond-mat/0110035,
title = {Close-packed dimers on nonorientable surfaces},
author = {Wentao T. Lu and F. Y. Wu},
journal= {arXiv preprint arXiv:cond-mat/0110035},
year = {2009}
}
Comments
13 pages, 1 figure, typo corrected to the version published in Phys. Lett. A 293, 235 (2002)