Pavlo Pylyavskyy, University of Minnesota


Talk Title: Ising model and the positive orthogonal Grassmannian

Talk abstract: Ising model is a classical model for ferromagnetism in
statistical mechanics. In a joint work with Pavel Galashin we
completely describe by inequalities the set of boundary correlation
matrices of planar Ising networks embedded in a disk. Specifically, we
give a simple bijection between such correlation matrices and points
in the totally nonnegative part of the orthogonal Grassmannian, which
has been introduced recently in the study of the scattering amplitudes
of ABJM theory.   Under our correspondence, Kramers--Wannier's
high/low temperature duality transforms into the cyclic symmetry of
the Grassmannian. We also show that the edge parameters of the Ising
model for reduced networks can be uniquely recovered from boundary correlations, solving the inverse problem.