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 N-c (d) that, for a given dimension d, separates a first-order region for N < N-c (d) from a second-order region for N > N-c (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 epsilon = 4 - d expansion and in contradiction with previous perturbative approaches performed at fixed dimension and with recent approaches based on the conformal bootstrap program.