Critical and Tricritical Wetting in the Two-Dimensional Blume–Capel model

Abstract

The two-dimensional Blume–Capel model with free surfaces where a surface field $$H_1$$ acts and the “crystal field” (controlling the density of the vacancies) takes a value $$D _s$$ different from the value $$D$$ in the bulk, is studied by Monte Carlo methods. Using a recently developed finite size scaling method that studies thin films in a $$L \times M$$ geometry with antisymmetric surface fields $$(H_L=-H_1)$$ and keeps a generalized aspect ratio $$c = L^2/M$$ constant, surface phase diagrams are computed for several typical choices of the parameters. It is shown that both second order and first order wetting transitions occur, separated by tricritical wetting behavior. The special role of vacancies near the surface is investigated in detail.