We study d-dimensional ferromagnetic spherical models with power-law, J(R)∼1/${\mathit{R}}^{\mathit{d}+\mathrm{\sigma }}$ (σ<2), or short-range (σ≃2) interactions and on-site terms of the form ${\mathit{Ds}}^2$-‖U‖${\mathit{s}}^4$+${\mathit{Vs}}^6$, and establish that the phase diagrams for all d and σ with σ<d<2σ, may exhibit critical end points terminating nonclassical critical lines; tricritical points may arise only for 3/2σ≤d. The phase boundary ${\mathit{D}}_{\mathrm{\sigma }}$(T,h), where h is the magnetic field, between the noncritical, spectator phase and the ordering and critical phase is shown to exhibit singularities at the end point with amplitudes obeying the universal ratio laws advanced on phenomenological grounds in Part I.

• Received 21 December 1990

DOI:https://doi.org/10.1103/PhysRevB.43.10635