Wedge covariance for 2D filling and wetting

A comprehensive theory of interfacial fluctuation effects occurring at 2D wedge (corner) filling transitions in pure (thermal disorder) and impure (random bond-disorder) systems is presented. Scaling theory and the explicit results of transfer matrix and replica trick studies of interfacial Hamiltonian models reveal that, for almost all examples of intermolecular forces, the critical behaviour at filling is fluctuation-dominated, characterised by universal critical exponents and scaling functions that depend only on the wandering exponent $\zeta$. Within this filling fluctuation (FFL) regime, the critical behaviour of the mid-point interfacial height, probability distribution function, local compressibility and wedge free energy are identical to corresponding quantities predicted for the strong-fluctuation (SFL) regime for critical wetting transitions at planar walls. In particular the wedge free energy is related to the SFL regime point tension which is calculated for systems with random-bond disorder using the replica trick. The connection with the SFL regime for all these quantities can be expressed precisely in terms of special wedge covariance relations which complement standard scaling theory and restrict the allowed values of the critical exponents for both FFL filling and SFL critical wetting.