LA Probability Forum

USC, Kaprelian (KAP) 414

It is a classical result of Groeneveld, Boel and Kasteleyn that boundary spin correlations functions in Ising models on planar graphs satisfy Pfaffian relations. Here we consider the reverse question, and show that any classical ferromagnetic spin model whose correlation functions satisfy Pfaffian relations must by (up to local simplifications of the graph) an Ising model on a planar graph. Our main tool is a new (coupled) version of the Edwards—Sokal representation of the Ising model applied to two independent copies of the spin model.