A note on wetting transition for gradient fields

We prove existence of a wetting transition for two classes of gradient fiel ds which include: (1) The Continuous SOS model in any dimension and (2) The massless Gaussian model in dimension 2. Combined with a recent result prov ing the absence of such a transition for Gaussian models above 2 dimensions (Bolthausen et al., 2000. J. Math. Phys. to appear), this shows in particu lar that absolute-value and quadratic interactions can give rise to complet ely different behavior. (C) 2000 Elsevier Science B.V. All rights reserved.