Planar graphical models which are easy
Michael Chertkov, Vladimir Chernyak · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2009
We describe a rich family of binary variables statistical mechanics models on planar graphs which are equivalent to Gaussian Grassmann Graphical models (free fermions). Calculation of partition function (weighted counting) in the models is easy (of polynomial complexity) as reduced to evaluation of determinants of matrixes linear in the number of variables. In particular, this family of models covers Holographic Algorithms of Valiant and extends on the Gauge Transformations discussed in our previous works.