A study of the phase diagram of symmeric binary Gaussian mixtures

We perform an analytic study of the main features of the phase diagram of symmetric binary Gaussian mixtures such that the range and strength of the interactions between particles of one species are the same as those of the other species. We focus on the relative locations of the spinodal and lambda-lines, i.e., the boundaries beyond which the uniform mixture becomes unstable respectively towards bulk demixing and microphase formation. We find that, when the lambda-line is present, three situations may occur: i) The spinodal line does not exist, and the lambda-line spans the whole concentration axis. ii) Both the lambda- and spinodal lines are present and span the whole concentration axis, but the spinodal instability is always preempted by the lambda-line. iii) The spinodal instability is the only one present at intermediate concentrations, but is preempted by the lambda- line at high and low concentrations.