Combinatorics of the Dimer Model on a Strip
Combinatorics
2007-09-12 v1 Statistical Mechanics
High Energy Physics - Theory
Abstract
In this note, we give a closed formula for the partition function of the dimer model living on a (2 x n) strip of squares or hexagons on the torus for arbitrary even n. The result is derived in two ways, by using a Potts model like description for the dimers, and via a recursion relation that was obtained from a map to a 1D monomer-dimer system. The problem of finding the number of perfect matchings can also be translated to the problem of finding a minmal feedback arc set on the dual graph.
Cite
@article{arxiv.0709.1546,
title = {Combinatorics of the Dimer Model on a Strip},
author = {D. Orlando and S. Reffert},
journal= {arXiv preprint arXiv:0709.1546},
year = {2007}
}
Comments
19 pages, 12 figures