  We consider the scaling limit of a generic ferromagnetic system with a
continuous phase transition, on the half plane with boundary conditions leading
to the equilibrium of two different phases below criticality. We use general
properties of low energy two-dimensional field theory to determine exact
asymptotics of the magnetization profile perperdicularly to the boundary, to
show the presence of an interface with endpoints pinned to the boundary, and to
determine its passage probability. The midpoint average distance of the
interface from the boundary grows as the square root of the distance between
the endpoints, unless the reflection amplitude of the bulk excitations on the
boundary possesses a stable bound state pole. The contact angle of the
phenomenological wetting theory is exactly related to the location of this
pole. Results available from the lattice solution of the Ising model are
recovered as a particular case.
