It is a famous result of statistical mechanics that, at low enough temperature, the random field Ising model is disorder relevant for d=2, i.e. the phase transition between uniqueness/non-uniqueness of Gibbs measures disappears, and disorder irrelevant otherwise (Aizenman-Wehr 1990). Generally speaking, adding disorder to a model tends to destroy the non-uniqueness of Gibbs measures.
In this talk we consider - in non-convex potential regime - a random gradient model with disorder in which the interface feels like a bulk term of random fields. We show that this model is disorder relevant with respect to the question of uniqueness of gradient Gibbs measures for a class of non-convex potentials and disorders. We also discuss the questions of decay of covariances and scaling limits for the model. No previous knowledge of gradient models will be assumed in the talk.
This is joint work with Simon Buchholz.[-]