Partial integration and local mean field approach for a vector lattice model of microemulsions: unbalanced case

We consider a vector lattice model for mixtures of water, oil and amphiphile, and it extends to the (unbalanced) case of different water and oil volume fractions, an approach previously developed for the balanced case. After an exact summation of the orientational degrees of freedom we get an effective hamiltonian with multi-site couplings, which is then studied in a local mean-field approximation. The phase diagram for several temperatures and strong amphiphilic interactions is mapped out both in terms of the chemical potentials and of the volume fractions of the components. We find several structured phases (lamellar, micellar and cubic) as well as homogeneous phases, and coexistence phenomena.