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 β-functions obtained within the minimal subtraction scheme without ε-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 occurring at three dimensions and provides elements towards a unified picture of all existing theoretical approaches to frustrated magnets.