title: Discovering and quantifying nontrivial fixed points in multi-field models.
abstract: We use the functional renormalization group and the [Formula: see text]-expansion concertedly to explore multicritical universality classes for coupled [Formula: see text] vector-field models in three Euclidean dimensions. Exploiting the complementary strengths of these two methods we show how to make progress in theories with large numbers of interactions, and a large number of possible symmetry-breaking patterns. For the three- and four-field models we find a new fixed point that arises from the mutual interaction between different field sectors, and we establish the absence of infrared-stable fixed-point solutions for the regime of small [Formula: see text]. Moreover, we explore these systems as toy models for theories that are both asymptotically safe and infrared complete. In particular, we show that these models exhibit complete renormalization group trajectories that begin and end at nontrivial fixed points.
authors.affiliation: Blackett Laboratory, Imperial College, London, SW7 2AZ UK.
authors.forename: A
authors.initials: A
authors.lastname: Eichhorn
authors.affiliation: Blackett Laboratory, Imperial College, London, SW7 2AZ UK ; King's College, London, UK.
authors.forename: T
authors.initials: T
authors.lastname: Helfer
authors.affiliation: Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, University of Bern, Sidlerstrasse 5, 3012 Bern, Switzerland.
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