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 R(d)(psi) depending only on the opening angle 2psi. R(d)(psi) 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.