  We propose a model for surfaces in mixtures of oil, water and surfactants
with strong electric dipoles. The dipole interactions give rise to a non-local
interaction with negative stiffness between surface elements. We show that, for
large space dimension D, this model has a phase transition from rough to smooth
surfaces. Contrary to models with a simple quadratic curvature energy of
positive sign, which always have a finite persistence length typical of rough
surfaces, the smooth surfaces in our model exhibit long-range correlations of a
generalized antiferromagnetic type. These correlations might be related to the
recently observed "egg carton" superstructure of membranes.
