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Monday, December 10th 2018

12:30 pm:

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.

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