Two-dimensional filling in ordered and disordered systems

We consider filling or wedge-wetting transitions occurring in a (1 + 1)-dim ensional wedge geometry with both thermal and random-bond disorder using ef fective interfacial Hamiltonian models. For ordered systems the problem may be solved using transfer-matrix methods for quite arbitrary choices of int erfacial binding potential and gives a complete classification of the possi ble critical behaviours. For random bonds the transition is studied for sho rt-ranged forces using the replica trick and the wedge-wetting critical exp onents are identified. Our results establish a remarkable relation between the mid-point height probability distribution PF(lo) at filling transitions and the appropriately defined height distribution function P-pi(l; theta(p i)) at planar wetting transitions. We observe that provided the wetting spe cific heat component alpha(s) = 0, then, in the scaling limit, P-F (l(0)) = P-pi(l; theta(pi) - alpha) where theta(pi) is the contact angle and alpha is the tilt angle of the wedge. This relation completely determines the all owed values of the filling critical exponents in the fluctuation-dominated regimes. Conjectures regarding interfacial fluctuation effects in finite-si ze two-dimensional systems are also made.