Phase diagram of a lattice microemulsion model

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Abstract
We derive the phase diagram of a recently proposed model of microemulsions. The model is equivalent to an Ising model with nearest-neighbor interaction parameter J, diagonal-neighbor interaction parameter 2M, and further-neighbor interaction parameter M. We find the regions of stability of the various phases in the j(=J/kT), m(=M/kT) plane, both by solution of the mean-field equations at finite j and m and by an exact analysis at T=0(m→−∞, j→±∞). The disordered (paramagnetic) region is bounded by an ellipse and two of its tangents. We concentrate our attention on the phases of periodic structure near the paramagnetic boundary, on the low-temperature phases, and on the connections between them.

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