Fluctuation-induced interactions between domains in membranes.

We study a model lipid bilayer composed of a mixture of two incompatible lipid types which have a natural tendency to segregate in the absence of membrane fluctuations. The membrane is mechanically characterized by a local bending rigidity kappa(phi) which varies with the average local lipid composition phi. We show, in the case where kappa varies weakly with phi, that the effective interaction between lipids of the same type either can be everywhere attractive or can have a repulsive component at intermediate distances greater than the typical lipid size. When this interaction has a repulsive component, it can prevent macrophase separation and lead to separation in mesophases with a finite domain size. This effect could be relevant to certain experimental and numerical observations of mesoscopic domains in such systems.