Abstract
It is shown that in the absence of a macroscopic external field, the direct correlation function in the planar interface between two fluid phases has a slow decay in the transverse directions. This is in contrast to all earlier assumptions and approximate results. More generally, when several fluid phases meet along a surface of contact, it is found that the direct correlation function decays slowly in the surface of contact. These results hold provided that self-maintained interfaces exist and the intermolecular forces decay rapidly enough at infinity.