Stiffness matrix formalism for wetting transitions .1. Short-range forces

Recent studies of complete wetting by a simple fluid at a planar substrate (wall) have emphasized the role of coupling between order parameter fluctuations near the wall and the depinning interface. These are modelled by a two-field effective Hamiltonian H-2[l(1),l(2)] characterized by a stiffness matrix Sigma(l(1),l(2)). The deep relationship between such model Hamiltonians and mean-field order-parameter correlations is reformulated in a simple matrix language and used to study details of correlation function structure related to the coupling of fluctuations. We uncover some new features of correlation function behaviour near the complete wetting transition, making connection with long-standing results and conjectures, and point out the significance of pairs of poles and zeros of the corresponding structure factor.