Theoretical study reveals the absence of stable fixed points in three-dimensional noncollinear magnets, indicating first-order phase transitions in physical systems.
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.
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Delamotte et al. (2016) studied this question.
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