Wedge covariance for two-dimensional filling and wetting

A comprehensive theory of interfacial fluctuation effects occurring at two-dimensional 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, characterized by universal critical exponents and scaling functions that depend only on the wandering exponent ζ. Within this filling-fluctuation (FFL) regime, the critical behaviour of the midpoint 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. The predictions for the values of the exponents in the SFL regime recover earlier results based on random walk arguments. The covariance of the wedge free energy leads to a new, general relation for the SFL regime point tension, which derives the conjectured Indekeu-Robledo critical exponent relation and also explains the origin of the logarithmic singularity for pure systems known from exact Ising studies due to Abraham and co-workers. Wedge covariance is also used to predict the numerical values of critical exponents and position dependence of universal one-point functions for pure systems.