Exact solutions in the two-dimensional wetting problem

Wetting transitions in two-dimensional lattice systems are considered. To obtain exact solutions the transfer-matrix method is used. Attention is focused on transitions at proper line defects (domain walls). The effective thickness of the wall increases as the transition point is approached, this being connected with growth of the intermediate (wetting) phase inside the domain wall. Depending on the types of transformations in the system of domain walls, the phase transitions can be first-order, second-order, or infinite-order. The general analysis makes it possible to apply the results obtained to the description of the behavior of the domain walls in the ANNNI model; in particular, the problem of the coexistence of a wetting transition and pinning of domain walls at an external boundary is considered.