Correlations in the liquid–vapor interface

A liquid–vapor system in a gravitational field is examined using the grand canonical distribution functions ρs(r1...rs) and direct correlation functions cs(r1...rs) for a nonuniform system. The limit of zero field is taken under the assumption that ρ1(z) approaches a limit representing a two-phase system. The limiting behavior is discussed in terms of an infinite continuous matrix calculated from c2(r1,r2) and ρ1(z). The vanishing of eigenvalues in zero field implies the appearance of long-ranged correlations. The correlations are shown to be in the horizontal directions, confined to the interface, and macroscopic in range. The situation in an interface is briefly contrasted with the effect of a rigid wall in order to illustrate the fact that spontaneous symmetry breaking rather than the inhomogeneity of ρ1(z) is responsbile for the long-ranged correlations. The invariance properties of a system in a gravitational field are used to give a new derivation of the conventional choice of the dividing surface. A microscopic expression for the surface tension is used to calculate the range of the interfacial correlations.