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arXiv · cond-mat/0505384

The 3D Dimer and Ising Problems Revisited

Martin Loebl·Lenka Zdeborova
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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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Martin Loebl, Lenka Zdeborova. 2005-05-16. The 3D Dimer and Ising Problems Revisited. https://doi.org/10.1016/j.ejc.2007.11.013

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