@article{Chernyak2009PlanarGM,
title={Planar Graphical Models which are Easy},
author={Vladimir Y. Chernyak and Michael Chertkov},
journal={CoRR},
year={2009},
volume={abs/0902.0320}
}

We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann graphical models (free fermions) defined on the same graph. Calculation of the partition function (weighted counting) for such a model is easy (of polynomial complexity) as it is reducible to evaluation of a Pfaffian of a matrix of size equal to twice the number of edges in the graph. In particular, this approach touches upon holographic algorithms of… CONTINUE READING