Title:
Some results for gradient fields with non-convex interactions

Abstract:
I will discuss scalar fields on the hypercubic lattice interacting
through two body V(phi_x-phi_y) for all pairs of nearest neighbors
<x,y>. The function V will be even, bounded below, with sufficient
growth at infinity. I will concentrate on the case of non-convex V
and discuss (1) possibility of multiple Gibbs measures (for the
same tilt) and (2) scaling limit of fluctuations in these measures.
I will mention a consequence between strict convexity of the
surface tension for the existence of Gibbs measure and
demonstrate an example where the surface tension is not
strictly convex.