Planar Graphical Models which are Easy

Details Planar Graphical Models which are Easy Planar Graphical Models which are Easy

Publishing date

2009-02-02

URL

arxiv.org/abs/0902.0320v5

Science

Physics

Field

Condensed Matter

SubField

Statistical Mechanics

Additional info

27 pages, 11 figures; misprints corrected

Type

Scientific paper

Abstract

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 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 Valiant and utilizes the Gauge Transformations discussed in our previous works.

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