Two-dimensional wetting transition in a corrugated potential

A simple model for the wetting or depinning transition of a two-dimensional solid-on-solid (SOS) interface in a short-range periodic pinning potential which alternates between attraction and infinite repulsion is analysed exactly. The interface is specified by transverse displacement variables xi which vary continuously in the interval x(min) < x(i) < infinity, and the stretching energy is proportional to Sigma(i) \x(i+1)-x(i)\. Both the semi-infinite and infinite geometries x(min) = 0, -infinity are considered. For the most part the wetting transition in the continuum model is similar to the transition in restricted SOS models with corrugated potentials, in which the xi are restricted to integers and x(i+1) - x(i) to +/-1, 0, but there are some qualitative differences in the phase diagrams involving re-entrant behaviour.