Statistical field theory for liquid vapor interface

Abstract

A statistical field theory for an inhomogeneous liquid, a planar liquid/vapor interface, is devised from first principles. The grand canonical partition function is represented via a Hubbard-Stratonovitch transformation leading, close to the critical point, to the usual φ4 scalar field theory which is then rigorously considered at the one-loop level. When further simplified it yields the well-known capillary wave theory without any ad hoc phenomenological parameter. Internal coherence of the one-loop approximation is discussed and good overall qualitative agreement with recent numerical simulations is stressed.