Absence of Phase Separation for Fluids in Three Dimensions

It is demonstrated that for short-range forces the density profile of the planar interface between fluid phases in three dimensions does not exist in the absence of a macroscopic external field such as gravity. This result holds for all nonzero values of the temperature and implies the absence of a roughening transition in continuous fluid interfaces in three dimensions, in contrast to the existence of such a transition in interfaces of three-dimensional lattice gases.