On Pfaffians in spin models

Marcin Lis
Technische Universität Wien

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.
Joint work with Diederik van Engelenburg.

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