The influence of non-locality on fluctuation effects for 3D short-ranged wetting

Abstract

We use a non-local interfacial Hamiltonian to revisit a number of problems associatedwith the fluctuation theory of critical wetting transitions in three-dimensionalsystems with short-ranged forces. These centre around previous renormalizationgroup predictions of strongly non-universal critical singularities and also possiblefluctuation-induced first-order (stiffness-instability) behaviour, based on localinterfacial models, which are not supported by extensive Monte Carlo simulations ofwetting in the three-dimensional Ising model. Non-locality gives rise to long-rangedtwo-body interfacial interactions controlling the repulsion from the wall not modelledcorrectly in previous interfacial descriptions. In particular, correlation functions arecharacterized by two diverging parallel correlation lengths, and , not one as previously thought. Mean-field, Ginzburg criterion and linear renormalization groupanalyses all show that some interfacial fluctuation effects are strongly damped for wavenumbersq>1/ξNL. This prevents a stiffness-instability and reduces the size of the asymptotic critical regimewhere non-universality can be observed. Non-universal critical singularities along thecritical wetting isotherm are determined by a smaller, effective value of the wettingparameter which slowly approaches its asymptotic limit as the wetting film grows. This isconfirmed by numerical simulation of a discretized version of the non-local model.