Global phase diagram for a three-component model

The global phase diagram in a five-dimensional parameter space is described for a model which can be thought of as the "regular-solution" model of a ternary mixture or the mean-field approximation to a spin-1 Ising ferromagnet with a general nearest-neighbor interaction (the Blume-Capel model). The model possesses three fourth-order critical points (known from previous work) which are connected to a total of nine lines of tricritical points. Four manifolds of four-phase coexistence occur along with three manifolds of double critical points and six manifolds of critical double-end points. The locations of all significant features of the phase diagram are described qualitatively, and quantitative results are provided for some of the manifolds of lower dimension. Computational procedures are described which permit a detailed exploration of any portion of the phase diagram which may be of interest