Stability of fixed points and generalized critical behavior in multifield models

We study models with three coupled vector fields characterized by $O(N_1)\oplus O(N_2) \oplus O(N_3)$ symmetry. Using the nonperturbative functional renormalization group, we derive $\beta$ functions for the couplings and anomalous dimensions in $d$ dimensions. Specializing to the case of three dimensions, we explore interacting fixed points that generalize the $O(N)$ Wilson-Fisher fixed point. We find a symmetry-enhanced isotropic fixed point, a large class of fixed points with partial symmetry enhancement, as well as partially and fully decoupled fixed point solutions. We discuss their stability properties for all values of $N_1, N_2$, and $N_3$, emphasizing important differences to the related two-field models. For small numbers of field components we find no stable fixed point solutions, and we argue that this can be attributed to the presence of a large class of possible (mixed) couplings in the three-field and multifield models. Furthermore, we contrast different mechanisms for stability interchange between fixed points in the case of the two- and three-field models, which generically proceed through fixed-point collisions.