Nonperturbative renormalization-group approach to frustrated magnets

This article is devoted to the study of the critical properties of classical XY and Heisenberg frustrated magnets in three dimensions. We first analyze the experimental and numerical situations. We show that the unusual behaviors encountered in these systems, typically nonuniversal scaling, are hardly compatible with the hypothesis of a second order phase transition. Moreover, the fact that the scaling laws are significantly violated and that the anomalous dimension is negative in many cases provides strong indications that the transitions in frustrated magnets are most probably of very weak first order. We then review the various perturbative and early nonperturbative approaches used to investigate these systems and argue that none of them provides a completely satisfactory description of the three-dimensional critical behavior. We then recall the principles of the nonperturbative approach-the effective average action method-that we have used to investigate the physics of frustrated magnets and show how it enables to clarify most of the problems encountered in the previous theoretical descriptions of frustrated magnets. First, we get an explanation of the long-standing mismatch between different perturbative approaches which consists in a nonperturbative mechanism of annihilation of fixed points between two and three dimensions. Secondly, we get a coherent picture of the physics of frustrated magnets in agreement with the numerical and experimental results. The central feature that emerges from our approach is the existence of scaling behaviors without fixed or pseudofixed point and that relies on a slowing down of the renormalization group flow in a whole region in the coupling constants space. This phenomenon allow us to explain the occurrence of generic weak first order behaviors and to understand the absence of universality in the critical behavior of frustrated magnets.