Effects of surface fluctuations in a two-dimensional emulsion

We investigate the role of geometrical shape fluctuations for the thermodynamic properties of a polydisperse ensemble of two-dimensional droplets. The energy of a droplet derives from the Hamiltonian for surface bending rigidity with spontaneous curvature. Interactions between individual droplets are omitted, but polydispersity in droplet size and arbitrarily large distortions of the droplet shape are incorporated fully. The physical property of self-avoidance is approximated by the less stringent topological requirement of unit winding number. This topological model shows that some physical observables are considerably more sensitive to the presence of shape fluctuations than others. The specific heat, in particular, is strongly affected by the presence of shape fluctuations. This observable is also very sensitive to approximate treatments of the shape fluctuations. The periodic Gaussian or Villain approximation is found to be reliable at all temperatures, whereas the Gaussian approximation fails except for very low temperatures.