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

Abstract

The effects of an off-diagonal quadratic symmetry-breaking field, $g$, on a three-component ($n=3$) 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 $\ensuremath{\epsilon}=4\ensuremath{-}d$. The phase diagrams are predicted to be realizable in certain $n=3$ cubic crystals undergoing structural phase transitions, such as BaTi${\mathrm{O}}_{3}$, RbCa${\mathrm{F}}_{3}$, and KMn${\mathrm{F}}_{3}$.