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