Gaussian curvature in an Ising model of microemulsions

We extend Widom’s Ising-like model of microemulsions on a simple cubic lattice by a new term which accounts for the Gaussian curvature energy of the oil–water interfaces. The new term distinguishes between different topologies of the interfaces and plays an important role in determining the microstructure of microemulsions on a scale larger or comparable to the persistence length provided that the microemulsion is dominated at all by curvature energies. We also speculate on its possible role for the breakdown of curvature energies in microemulsions.