On the nature of the phase transition of helimagnets

Abstract

There is a controversy about the nature of the phase transition that occurs in Helimagnets. Early renormalization group calculations, on the appropriate Landau–Ginzburg Hamiltonian in D=4−ε led to no fixed point. This fact has been interpreted as the occurrence of a first-order phase transition in these models. However, results on recent Monte Carlo simulations on stacked triangular antiferromagnets are in favor of a continuous transition in three-dimensions with critical exponents different from those of the standard O(N) models. On the basis of these results, it has been conjectured that a stable fixed point should occur in 3D which is unreachable by perturbation theory near 4D. As a consequence, a new universality class for helimagnets and related frustrated spin systems was proposed. Another general strategy available to study the critical behavior of these systems is the perturbative expansion near 2D of a suited nonlinear sigma model. A fixed point that is O(4) symmetric is found by means of a 2+ε expansion. Thus, if a stable fixed point is likely to occur in D=3, it should be of the N=4 universality class. A simple scenario is proposed that is in agreement with both 4−ε and 2+ε results: Helimagnets can undergo, according to their microscopic Hamiltonian, a first-order transition or a second-order one with either N=4 or tricritical mean-field exponents. It is argued that this view is supported by experimental data.