title: Stability of fixed points and generalized critical behavior in multifield models.
abstract: We study models with three coupled vector fields characterized by O(N_{1})⊕O(N_{2})⊕O(N_{3}) symmetry. Using the nonperturbative functional renormalization group, we derive β 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.
authors.affiliation: Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, N2L 2Y5 Ontario, Canada.
authors.forename: A
authors.initials: A
authors.lastname: Eichhorn
authors.affiliation: Physics Department, University of Illinois at Chicago, 845 West Taylor Street, Chicago, Illinois 60607, USA.
authors.forename: D
authors.initials: D
authors.lastname: Mesterházy
authors.affiliation: Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany.
authors.forename: M M
authors.initials: MM
authors.lastname: Scherer