Coupled Hamiltonians and three-dimensional short-range wetting transitions

We address three problems faced by effective interfacial Hamiltonian models of wetting based on a single collective coordinate ℓ(y) representing the position of the unbinding fluid interface. Problems (P1) and (P2) refer to the predictions of non-universality at the upper critical dimension d=3 at critical and complete wetting, respectively, which are not borne out by Ising model simulation studies. (P3) relates to mean-field correlation function structure in the underlying continuum Landau model. Building on earlier work by Parry and Boulter we investigate the hypothesis that these concerns arise due to the coupling of order parameter fluctuations near the unbinding interface and wall. For quite general choices of collective coordinates Xi(y) we show that arbitrary two-field models H[X1,X2] can recover the required anomalous structure of mean-field correlation functions (P3). To go beyond mean-field theory we introduce a set H of Hamiltonians based on proper collective coordinates s(y) near the wall which have both interfacial and spin-like components. We argue that an optimum model H[s,ℓ]∈H, in which the degree of coupling is controlled by an angle like variable δ∗, best describes the non-universality of the Ising model and investigate its critical behaviour. For critical wetting the appropriate Ginzburg criterion shows that the true asymptotic critical regime for the local susceptibility χ1 is dramatically reduced consistent with observations of mean-field behaviour in simulations (P1). For complete wetting the model yields a precise expression for the temperature dependence of the renormalised critical amplitude θ in good agreement with simulations (P2). We highlight the importance of a new wetting parameter which describes the physics that emerges due to the coupling effects.