Three-component model and tricritical points: A renormalization-group study. II. General dimensions and the three-phase monohedron

In Part I the global phase diagram of the general spin-1, nearest-neighbor, ferromagnetic Ising model was studied for $d=2\mathrm{}$ dimensions using an approximate renormalization-group approach of the Migdal-Kadanoff type. Here general $d$ is considered with emphasis on $\epsilon =d-1\mathrm{}$ expansions and on the variation of the tricritical exponents with $d<~4$. A dilution field is introduced which can be chosen to yield tricritical exponents for $d=2\mathrm{}$, in better agreement with more reliable estimates and conjectured exact results. The three-phase monohedra, which describe the densities of coexisting phases near a tricritical point, are calculated quantitatively for $d=2\mathrm{}$, and their shape contrasted with that predicted by classical theory: they are found, in particular, to be significantly flattened.