Large deviations for the random field of gradients and their thermodynamic properties

The study of effective interface models have started with continuous Ising models. The interface is modelled as a random height function representing the distance of the interface from a reference height. The interaction depends only on the gradient, hence due to the rich symmetry phase transitions occur. For the latter one needs that the interaction is strictly convex, because this ensure the existence of infinite Gibbs measures at least for dimension greater equal than three. If one consider the so-called random field of gradients (of the height functions) they exist for any dimension.

In the talk we present a new approach for the random field of gradients and a large deviation result for the free boundary case. We show the existence of the specific entropy and free enrgy. We further discuss various problems connected with boundary conditions and outline the motivation for studying non convex interactions.

The talk is based on work with Deuschel and Sheffield.