MIT Probability Seminar
Monday, October 18, 2021 at 4:15pm to 5:15pm
Building 2, Room 2-147
182 MEMORIAL DR, Cambridge, MA 02139
Speaker: Matan Harel - Northeastern University
Title: Quantitative estimates on the effect of random disorder on low-dimensional lattice models.
Abstract: In their seminal work, Imry and Ma predicted that the addition of an arbitrarily small random external field to a low-dimensional statistical physics model causes the usual first-order phase transition to be `rounded-off.' This phenomenon was proven rigorously by Aizenman and Wehr in 1989 for a vastly general class of spin systems and random perturbations. Recently, the effect was quantified for the random-field Ising model, proving that it exhibits exponential decay of correlations at all temperatures. Unfortunately, the analysis relies on the monotonicity (FKG) properties which are not present in many other classical models of interest. This talk will present quantitative versions of the Aizenman-Wehr theorems for general spin systems with random disorder, including Potts, spin O(n), spin glasses, and random surface models. This is joint work with Paul Dario and Ron Peled.
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