Cornell University

Mathematics Lie Groups Seminar

Friday, November 16, 2018 at 3:30pm

Malott Hall, 406

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.

Event Type

Seminar

Departments

Mathematics

Website

https://math.cornell.edu/

Contact E-Mail

mlt39@cornell.edu

Contact Name

Melissa Totman

Contact Phone

607-254-8993

Speaker

Pavlo Pylyavskyy

Speaker Affiliation

University of Minnesota

Dept. Web Site

https://math.umn.edu/directory/pavlo-pylyavskyy

Disability Access Information

If you need any special accommodations (e.g., dietary constraints, mobility constraints, etc.), please contact Heather Peterson

Open To

Public

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