Fluctuation phenomena in the tricritical behavior of two models with tensor order parameter

The fluctuation theory of phase transitions is used to study tricritical behavior in the isotropic phase of two models in which the order parameter is a $p$-dimensional symmetric traceless tensor. For arbitrary values of $p$, differential equations are obtained for the vertex functions from the second to the sixth orders as functions of the reciprocal susceptibility. The cases $p=1,2,3$ are studied. For $p=1,2$, the models exhibit tricritical behavior. For $p=3$, allowance for fluctuations leads in the general case to the appearance of instability in the critical behavior of the models and to the replacement of tricritical behavior by a phase transition of the first kind.