Tricritical wedge filling transitions with short-ranged forces

We show that the 3D wedge filling transition in the presence of short-ranged interactions can be first-order or second order depending on the strength of the line tension associated with to the wedge bottom. This fact implies the existence of a tricritical point characterized by a short-distance expansion which differs from the usual continuous filling transition. Our analysis is based on an effective one-dimensional model for the 3D wedge filling which arises from the identification of the breather modes as the only relevant interfacial fluctuations. From such analysis we find a correspondence between continuous 3D filling at bulk coexistence and 2D wetting transitions with random-bond disorder.