Decay of covariances, uniqueness of ergodic component and scaling limit for a class of \nablaϕsystems with non-convex potential

Abstract

We consider a gradient interface model on the lattice with interaction potential which is a nonconvex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for \nablaϕ-Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.

41 pages, 5 figures