Wedge filling and interface delocalization in finite Ising lattices with antisymmetric surface fields

Theoretical predictions by Parry et al. for wetting phenomena in a wedge geometry are tested by Monte Carlo simulations. Simple cubic L×L×Ly Ising lattices with nearest neighbor ferromagnetic exchange and four free L×Ly surfaces, at which antisymmetric surface fields ±Hₛ act, are studied for a wide range of linear dimensions (4<~L<~320,30<~Ly<~1000), in an attempt to clarify finite size effects on the wedge filling transition in this ``double-wedge'' geometry. Interpreting the Ising model as a lattice gas, the problem is equivalent to a liquid-gas transition in a pore with quadratic cross section, where two walls favor the liquid and the other two walls favor the gas. For temperatures T below the bulk critical temperature Tc this boundary condition (where periodic boundary conditions are used in the y direction along the wedges) leads to the formation of two domains with oppositely oriented magnetization and separated by an interface. For L,Ly→∞ and T larger than the filling transition temperature Tf(Hₛ), this interface runs from the one wedge where the surface planes with a different sign of the surface field meet (on average) straight to the opposite wedge, so that the average magnetization of the system is zero. For T<Tf(Hₛ), however, this interface is bound either to the wedge where the two surfaces with field -Hₛ meet (then the total magnetization m of the system is positive) or to the opposite wedge (then $m<0).$ The distance l₀ of the interface midpoint from the wedges is studied as →TTf(Hₛ) from below, as is the corresponding behavior of the magnetization and its moments. We consider the variation of l₀ for T>Tf(Hₛ) as a function of a bulk field and find that the associated exponents agree with theoretical predictions. The correlation length ξy in the y direction along the wedges is also studied, and we find no transition for finite L and Ly→∞. For →L∞ the prediction l₀∝(Hsc-Hₛ)^-1/4 is verified, where Hsc(T) is the inverse function of Tf(Hₛ) and ξy∝(Hsc-Hₛ)^-3/4, respectively. We also find that m vanishes discontinuously at the filling transition. When the corresponding wetting transition is first order we also obtain a first-order filling transition.