Fluctuation-induced first-order transitions and symmetry-breaking fields. II. Systems with no stable fixed points

The crossover from first order to continuous transition induced by symmetry-breaking field, $g$, is analyzed for several models possessing no stable fixed point. Specifically, the ($g,T$) phase diagram associated with $n=6\mathrm{}$ type-I fcc antiferromagnets (such as U${\mathrm{O}}_2$) and with $n=4\mathrm{}$ type-II fcc antiferromagnets (such as TbP, TbAs, CeTe, and TbSe) is considered. The symmetry-breaking field $g$ corresponds to a magnetic field or to a uniaxial stress in certain symmetry directions. The phase diagrams are studied using large-$g$ expansions, mean-field calculations, and renormalization-group techniques in $d=4-\epsilon$ dimensions. It is found that in both cases the phase diagram is rather complex exhibiting tricritical points and critical end points.