Speaker:
Marcin Lis, Vienna University of Technology
Abstract
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 be
(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.
Joint work with Diederik van Engelenburg.