Critical effects at 3D wedge wetting

We show that continuous filling transitions are possible in 3D wedge geometries made from substrates exhibiting first-order wetting transitions, and develop a fluctuation theory yielding a complete classification of the critical behavior. Our fluctuation theory is based on the derivation of a Ginzburg criterion for filling and also on an exact transfer-matrix analysis of a novel effective Hamiltonian that we propose as a model for wedge fluctuation effects. The influence of interfacial fluctuations is very strong and, in particular, leads to a remarkable universal divergence of the interfacial roughness xi(perpendicular to) similar to (T-F - T)(-1/4) on approaching the filling temperature T-F, valid for all possible types of intermolecular forces.