  We consider two dimensional dispersions of droplets of isotropic phase in a
liquid with an XY-like order parameter, tilt, nematic, and hexatic symmetries
being included. Strong anchoring boundary conditions are assumed. Textures for
a single droplet and a pair of droplets are calculated and a universal
droplet-droplet pair potential is obtained. The interaction of dispersed
droplets via the ordered phase is attractive at large distances and repulsive
at short distances, which results in a well defined preferred separation for
two droplets and topological stabilization of the emulsion. This interaction
also drives self-assembly into chains. Preferred separations and energy
barriers to coalescence are calculated, and effects of thermal fluctuations and
film thickness are discussed.
