Three-dimensional wetting revisited

Abstract

We review progress made towards resolving long-standing problems associated with the theory of wetting transitions in three-dimensional systems with short-ranged forces (corresponding to the marginal dimension). We begin by emphasizing the importance of two seemingly unrelated problems faced by the standard (capillary-wave) effective interfacial Hamiltonian model: (a) the discrepancy with the results of Monte Carlo simulation studies of the critical wetting transition in the Ising model which do not reveal any of the predicted non-universal behaviour; (b) the failure of the interfacial model to describe the structure of correlation functions (at the wall) known from mean-field studies of the complete wetting transition. Recent work suggests that these problems may be overcome by introducing new effective Hamiltonians which improve on the capillary-wave model and lead to novel fluctuation effects in d = 3. The new models follow directly from the development of much improved systematic techniques concerning their derivation and justification initiated by Fisher and Jin. These workers emphasized the importance of allowing for the position dependence of the stiffness coefficient and showed that it may drive a (bare) critical wetting transition first order. This has been further developed by Parry, Boulter and co-workers who argue that it is essential to model the coupling of order-parameter fluctuations at the wall and interface and show how this resolves problem (b). The coupled Hamiltonian also leads to new predictions for fluctuation effects in d = 3 which are in good agreement with more recent Ising model simulations by Binder and co-workers as well as providing a likely explanation for problem (a).