A transfer matrix approach to the 3D wetting and pinning problems

We consider the pinning of an interface on a 3D lattice by an edge potential (semi-infinite geometry). This situation models the wetting transition occurring in such physical systems as binary fluids or adsorbed gases. The transfer matrix method is used to get exact results on strips of finite width; we propose a way of extrapolating them and of deriving the phase diagram of the infinite system. The mechanism of the transition changes when the pinning and roughening temperatures coincide.