Fluctuation-induced first-order transitions and symmetry-breaking fields. I. Cubic model

A model Hamiltonian for which a stable fixed point is not accessible is expected to yield a first-order transition. By applying a symmetry-breaking field, a continuous transition may be restored. The crossover from first-order to continuous transition induced by the most general quadratic symmetry-breaking field, $g$, for an $n=2\mathrm{}$ cubic model, is studied using large-$g$ expansion, mean-field, and renormalization-group calculations. It is shown that the ($g,T$) phase diagram is rather complex, exhibiting tricritical, fourth-order critical, and critical end points. This phase diagram may be realized in certain compounds corresponding to $n=2\mathrm{}$ and $n=3\mathrm{}$ cubic models such as ${\mathrm{Tb}}_2$ ${\left(\mathrm{M}\mathrm{o}{\mathrm{O}}_4\right)}_3$, BaTi${\mathrm{O}}_3$, RbCa${\mathrm{F}}_3$, and KMn${\mathrm{F}}_3$.