Interfacial adsorption in the two-dimensional blume-capel model

New Monte Carlo (MC) results on the interfacial adsorption in the vicinity of the tricritical point of the two-dimensional Blume-Capel model are reported. The net adsorption, W₀, is found to diverge as W₀ approximately t_c^-w with omega =0.44+or-0.02 as the tricritical point is approached along a path asymptotically not parallel to the phase boundary. This behaviour as well as previous MC results on the interfacial adsorption at the critical line and the first-order transition of the model are explained using analytic and scaling arguments. In addition, finite size effects at the first-order transition are analysed, and it is shown that the critical adsorption scales as L_{perpendicular to}f(L/sub ////L _{perpendicular to}²) where L/sub /// and L _{perpendicular to} are the lengths of the system in the directions parallel and perpendicular to the interface. The scaling function f is evaluated by performing MC simulations on systems with various length to width ratios.