The 3D Dimer and Ising Problems Revisited
Martin Loebl, Lenka Zdeborova
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.
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