We address three problems faced by effective interfacial Hamiltonian models
of wetting based on a single collective coordinate \ell 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. 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 X_i we show that arbitrary two-field models H[X_1,X_2] can recover
the required anomalous structure of mean-field correlation functions (P3). To
go beyond mean-field theory we introduce a set of Hamiltonians based on proper
collective coordinates s near the wall which have both interfacial and
spin-like components. We argue that an optimum model H[s,\ell] in which the
degree of coupling is controlled by an angle-like variable, 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 \chi_1 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 renormalized critical amplitude \theta 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.Comment: 34 pages, RevTex, 8 eps figures. To appear in Physica
