Fluctuation-induced first-order transitions and symmetry-breaking fields: Then=3-component cubic model

The effects of an off-diagonal quadratic symmetry-breaking field, $g$, on a three-component ($n=3\mathrm{}$) cubic model with no accessible fixed points are studied. It is shown that this perturbation induces a crossover from first-order to continuous transition. Depending upon the initial values of the parameters characterizing the model, two types of ($g,T$) phase diagrams are possible, both of which are rather complex, exhibiting tricritical, critical, and critical end points. The ($g,T$) phase diagrams are studied using large-$g$ expansion, mean-field theory, and renormalization-group analysis. A universal amplitude ratio associated with the critical end points is calculated to leading (zeroth) order in $\epsilon =4-d$. The phase diagrams are predicted to be realizable in certain $n=3\mathrm{}$ cubic crystals undergoing structural phase transitions, such as BaTi${\mathrm{O}}_3$, RbCa${\mathrm{F}}_3$, and KMn${\mathrm{F}}_3$.