The 3D Dimer and Ising Problems Revisited

Details The 3D Dimer and Ising Problems Revisited The 3D Dimer and Ising Problems Revisited

2005-05-16

arxiv.org/abs/cond-mat/0505384v1

Eur.J.Combinatorics29:966-978,2008

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1016/j.ejc.2007.11.013

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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