Planar graphical models which are easy

Vladimir Y. Chernyak, Michael Chertkov

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 Valiant and utilizes the gauge transformations discussed in our previous works.

Original languageEnglish
Article numberP11007
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number11
Publication statusPublished - Nov 2010
Externally publishedYes


  • Analysis of algorithms
  • Gauge theories
  • Rigorous results in statistical mechanics


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