COMPLETE WETTING IN 3 DIMENSIONS .1. 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 H-I((2))[l(1), l(2)] which is a functional of two collective coordinates in order to properly describe the coupling between fluctuations near the wall and the depinning fluid (alpha beta) interface. This gives an accurate description of the Omstein-Zemike-like fluctuations of particles located near the alpha beta interface and the non-Omstein-Zernike behaviour of correlations near the wall. We show that the off-diagonal elements of the stiffness matrix characterizing H-I((2))) [l(1), l(2)] are related to singular behaviour of the free-energy.