The 3D Dimer and Ising Problems Revisited
arXiv:cond-mat/0505384 · doi:10.1016/j.ejc.2007.11.013
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.