Fluctuations, correlation functions and interfacial Hamiltonians for the complete wetting phase transition

Abstract

Exact statistical mechanical sum rules are combined with thermodynamic scaling arguments to determine the leading-order singular contributions to the transverse moments of the density-density correlation function G of a simple fluid undergoing a complete wetting phase transition, from off-bulk coexistence, at a structureless substrate (wall). Contrary to our earlier suggestion, capillary-wave-like fluctuations do manifest themselves throughout the wetting film and lead to a transverse correlation length ξ‖(a), for both particles near the wall, which diverges with the same critical exponent as ξ‖, the correlation length appropriate for both particles in the depinning liquid-gas interface. Explicit results from a mean-field (density functional) calculation are consistent with our general predictions. In the weak fluctuation regime (d < 3), scaling methods are used to derive the short distance expansions of the density profile and moments of G for short ranged forces. These expansions, which describe singula...