Wedgecovariance for two-dimensional filling and wetting

Abstract

A comprehensive theory of interfacial fluctuation effectsoccurring at two-dimensional wedge (corner) filling transitions in pure(thermal disorder) and impure (random bond disorder) systems ispresented. Scaling theory and the explicit results of transfermatrix and replica trick studies of interfacial Hamiltonianmodels reveal that, for almost all examples of intermolecularforces, the critical behaviour at filling isfluctuation dominated, characterized by universal criticalexponents and scaling functions that depend only on thewandering exponent ζ. Within this filling-fluctuation (FFL) regime, the critical behaviour of themidpoint interfacial height, probability distribution function,local compressibility and wedge free energy are identical tocorresponding quantities predicted for the strong-fluctuation (SFL) regime for critical wetting transitions atplanar walls. In particular the wedge free energy is related tothe SFL regime point tension, which is calculated for systemswith random bond disorder using the replica trick. Theconnection with the SFL regime for all these quantities can beexpressed precisely in terms of special wedge covariancerelations, which complement standard scaling theory and restrictthe allowed values of the critical exponents for both FFLfilling and SFL critical wetting. The predictions for the valuesof the exponents in the SFL regime recover earlier results basedon random walk arguments. The covariance of the wedge freeenergy leads to a new, general relation for the SFL regime pointtension, which derives the conjectured Indekeu-Robledo criticalexponent relation and also explains the origin of thelogarithmic singularity for pure systems known from exact Isingstudies due to Abraham and co-workers. Wedge covariance is alsoused to predict the numerical values of critical exponents andposition dependence of universal one-point functions for puresystems.