The 3D Dimer and Ising Problems Revisited
Statistical Mechanics
2008-11-26 v1 High Energy Physics - Theory
Abstract
We express the finite 3D Dimer partition function as a linear combination of determinants of oriented adjacency matrices, and the finite 3D Ising partition sum as a linear combination of products over aperiodic closed walks. The methodology we use is embedding of cubic lattice on 2D surfaces of large genus.
Cite
@article{arxiv.cond-mat/0505384,
title = {The 3D Dimer and Ising Problems Revisited},
author = {Martin Loebl and Lenka Zdeborova},
journal= {arXiv preprint arXiv:cond-mat/0505384},
year = {2008}
}