Planar Graphical Models which are Easy

@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

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