Tricritical coexistence in three dimensions: The multicomponent limit

The asymptotic tricritical equation of state, including the three-phase coexistence monohedron, is analyzed in detail for the exactly soluble multicomponent or spherical limit, $n\to \infty$, of the continuous-spin model with terms of order $s^3$, $s^4$, and $s^6$, in $d=3\mathrm{}$ spatial dimensions. Various nonuniversal scaling functions and amplitude ratios, depending on the range parameter $z\propto \frac{1}{R_0^3}$, are evaluated explicitly and reveal the nature and magnitude of the deviations from the classical, phenomenological theory of tricriticality (which is developed systematically in an Appendix). The relationship to results for finite $n$ is discussed briefly.