Matan Harel

Quantitative estimates on the effect of disorder on low-dimensional lattice models

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. This is joint work with Paul Dario and Ron Peled.