Kastelyn in the 1960's continuing Onsanger's work on the Ising model, found combinatorial solutions to the 2 dimensional planar Ising model. This was for undirected graphs.
Has a similar algorithm been found for planar directed graphs?
To clarify what I mean, although there are several different ways one could generalise the planar Ising model to directed graphs, I have in the mind the following:
The 2-local term in the standard Ising model is the symmetric matrix $J_{ij}$. The directed graph would be represented by unsymmetric matrix $J_{ij}$! So the sum over the partition function would be unsymmetrical. I hope this helps.