Fixed points in frustrated magnets revisited

TL;DR

This paper critically examines perturbative renormalization group estimates for frustrated magnets, revealing that the presumed fixed point is likely unphysical and supporting a weak first order transition in three dimensions.

Contribution

Reevaluates five-loop beta-functions for frustrated magnets, demonstrating the unphysical nature of the fixed point and confirming the weak first order transition.

Findings

The fixed point is likely unphysical.

Supports the weak first order transition at three dimensions.

Provides a unified theoretical perspective.

Abstract

We analyze the validity of perturbative renormalization group estimates obtained within the fixed dimension approach of frustrated magnets. We reconsider the resummed five-loop beta-functions obtained within the minimal subtraction scheme without epsilon-expansion for both frustrated magnets and the well-controlled ferromagnetic systems with a cubic anisotropy. Analyzing the convergence properties of the critical exponents in these two cases we find that the fixed point supposed to control the second order phase transition of frustrated magnets is very likely an unphysical one. This is supported by its non-Gaussian character at the upper critical dimension d=4. Our work confirms the weak first order nature of the phase transition occuring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.