PARTIAL INTEGRATION AND LOCAL MEAN-FIELD APPROACH FOR A VECTOR LATTICE MODEL OF MICROEMULSIONS

A vector model on the simple cubic lattice, describing a mixture of wa ter, oil, and amphiphile, is considered. An integration over the amphi phile orientational degrees of freedom is performed exactly in order t o obtain an effective Hamiltonian for the system. The resulting model is a three-state (spin-1) system and contains many-site interaction te rms. The analysis of the ground state reveals the presence of the wate r-oil-rich phase as well as the amphiphile-rich and the cubic phases. The temperature phase diagram of the system is analyzed in a local mea n-field approach, and a triple line of water-rich, oil-rich, and micro emulsion coexistence is obtained. For some values of the model paramet ers, lamellar phases also appear in the system, but only at finite tem perature. The Lifshitz line is determined in a semianalytical way in o rder to locate the microemulsion region of the disordered phase.