The global phase diagram in a five-dimensiona1 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-1Ising ferromagnet with a general nearest-neighbor interaction (the Blurne-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.

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Exact renormalization-group recursion relations are studied for a spin-1 Ising model in one dimension. In this model, critical lines are marked by a double degeneracy of the largest eigenvalue of the transfer matrix, and the tricritical point by a triple degeneracy. This is directly related to the tricritical fixed point being more unstable than the critical fixed points.