Complete wetting in three dimensions I. Connection between correlation functions and generalized effective Hamiltonian theory

We study the pair correlation function for an inhomogeneous fluid or Ising-type spin system near a wall with particular attention to the complete wetting phase transition. We show that one can unify a generalized interfacial Hamiltonian theory with a mean-field treatment of correlations provided we follow a systematic scheme for reconstructing order-parameter fluctuations. Near a complete wetting transition it is necessary to use a model effective Hamiltonian HI(2) [l1, l2] which is a functional of two collective coordinates in order to properly describe the coupling between fluctuations near the wall and the depinning fluid (αβ) interface. This gives an accurate description of the Ornstein-Zernike-like fluctuations of particles located near the αβ interface and the non-Ornstein-Zernike behavior of correlations near the wall. We show that the off-diagonal elements of the stiffness matrix characterizing HI(2) [l1, l2] are related to singular behaviour of the free-energy.