Solvable models of corner wetting in two and three dimensions

Corner wetting is studied in systems with short-range interactions using a solid-on-solid approximation to the nearest-neighbor Ising model. Complete wetting models are described by the generating functions for linear [two dimensions (2D)] and plane [three dimensions (3D)] partitions. The wetted area (volume in 3D) is found to behave as 〈A〉~1H² (2D) and 〈V〉~1H³ (3D), as a function of the bulk field H. In the presence of surface pinning potentials on two edges of an n×n square array, we find that corner wetting occurs in two stages. The edge with weaker pinning wets first via a first-order transition, and at a second, higher temperature, the edge with stronger pinning wets via a second-order (Abraham) transition.