Correlation functions in the capillary wave model of the liquid–vapor interface

We study the capillary wave model of the liquid–vapor interface and derive expressions valid in arbitrary dimensions for the density profile and the density–density pair correlation function. The latter is inverted to give an explicit expression for the direct correlation function. We examine the effects of long wavelength density fluctuations on these functions in dimensions d3 and discuss the applicability of the model to a real liquid–vapor system.