Multicritical behavior in frustrated spin systems with non-collinear order

We investigate the phase diagram and, in particular, the nature of the multicritical point in three-dimensional frustrated N-component spin models with non-collinear order in the presence of an external field, for instance easy-axis stacked triangular antiferromagnets in the presence of a magnetic field along the easy axis. For this purpose we study the renormalization-group flow in a Landau-Ginzburg-Wilson ϕ4 theory with symmetry O(2)⊗[Z2⊕O(N−1)] that is expected to describe the multicritical behavior. We compute its MS¯β functions to five loops. For N⩾4, their analysis does not support the hypothesis of an effective enlargement of the symmetry at the multicritical point, from O(2) ⊗ [Z2⊕O(N−1)] to O(2) ⊗ O(N). For the physically interesting case N=3, the analysis does not allow us to exclude the corresponding symmetry enlargement controlled by the O(2) ⊗ O(3) fixed point. Moreover, it does not provide evidence for any other stable fixed point. Thus, on the basis of our field-theoretical results, the transition at the multicritical point is expected to be either continuous and controlled by the O(2) ⊗ O(3) fixed point or to be of first order.