Universal phase boundary shifts for corner wetting and filling

The phase boundaries for corner wetting (filling) in square and diagonal lattice Ising models are exactly determined and show a universal shift relative to wetting near the bulk criticality. More generally, scaling theory predicts that the filling phase boundary shift for wedges and cones is determined by a universal scaling function Rd(ψ) depending only on the opening angle 2ψ. Rd(ψ) is determined exactly in d = 2 and approximately in higher dimensions using nonclassical local functional and mean-field theory. Detailed numerical transfer matrix studies of the magnetization profile in finite-size Ising squares support the conjectured connection between filling and the strong-fluctuation regime of wetting.