Functional renormalization group approach to noncollinear magnets

A functional renormalization group approach to d-dimensional, N-component, noncollinear magnets is performed using various truncations of the effective action relevant to study their long distance behavior. With help of these truncations we study the existence of a stable fixed point for dimensions between d=2.8 and d=4 for various values of N focusing on the critical value Nc(d) that, for a given dimension d, separates a first-order region for N<Nc(d) from a second-order region for N>Nc(d). Our approach concludes to the absence of a stable fixed point in the physical - N=2,3 and d=3 - cases, in agreement with the ε=4-d expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on the conformal bootstrap program.