Dimers on graphs in non-orientable surfaces
Mathematical Physics
2012-08-09 v3 Geometric Topology
math.MP
Abstract
The main result of this paper is a Pfaffian formula for the partition function of the dimer model on a graph G embedded in a closed, possibly non-orientable surface S. This formula is suitable for computational purposes, and it is obtained using purely geometrical methods. The key step in the proof consists of a correspondence between some orientations on G and the set of pin^- structures on S. This generalizes (and simplifies) the results of a previous paper [2].
Cite
@article{arxiv.0804.4772,
title = {Dimers on graphs in non-orientable surfaces},
author = {David Cimasoni},
journal= {arXiv preprint arXiv:0804.4772},
year = {2012}
}
Comments
27 pages, 5 figures; minor changes in v3