Non-Gaussian surface pinned by a weak potential

We consider a model of a two-dimensional interface of the (continuous) SOS type, with finite-range, strictly convex interactions. We prove that, under an arbitrarily weak pinning potential, the interface is localized. We cons ider the cases of both square well and delta potentials. Our results extend and generalize previous results for the case of nearest neighbours Gaussia n interactions in [7] and [1]. We also obtain the tail behaviour of the hei ght distribution, which is not Gaussian.