Student Probability Seminar

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The Dobrushin Interface for the 3-d Ising Model

Speaker: Joseph Chen, CIMS

Location: Warren Weaver Hall 312

Date: Tuesday, April 26, 2022, 9:50 a.m.

Synopsis:

The 3-d Ising model with Dobrushin boundary conditions considers the Ising model on an infinite cylinder with “-“ boundary conditions on the upper half space and “+” boundary conditions on the lower half space. The result inside the cylinder will thus be an ocean of minus spins and an ocean of plus spins, and where they meet lies an interface (which one can think of as a deformed plane, separating the minus spins from the plus spins). I will review Dobrushin’s paper (1972) proving that the interface remains “flat” even as we take the cylinder width to infinity. The significance of this result is that it provided the first example of a non-translationally invariant Gibbs measure on Z^3, as well as the first example of coexistence.