Multicritical behavior in frustrated spin systems with noncollinear order

TL;DR

This paper studies the multicritical behavior of three-dimensional frustrated spin systems with noncollinear order, using high-loop renormalization-group calculations to analyze symmetry and phase transition nature.

Contribution

It provides a five-loop renormalization-group analysis of the multicritical point, clarifying the symmetry and transition type in frustrated spin models with noncollinear order.

Findings

For N≥4, no symmetry enlargement at the multicritical point.

For N=3, symmetry enlargement to O(2)xO(3) cannot be excluded.

Transition is either continuous (O(2)xO(3) fixed point) or first order.

Abstract

We investigate the phase diagram and, in particular, the nature of the the multicritical point in three-dimensional frustrated $N$-component spin models with noncollinear 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 \phi^4 theory with symmetry O(2)x[Z_2 +O(N-1)] that is expected to describe the multicritical behavior. We compute its MS \beta functions to five loops. For N\ge 4, their analysis does not support the hypothesis of an effective enlargement of the symmetry at the multicritical point, from O(2) x [Z_2+O(N-1)] to O(2)xO(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)xO(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)xO(3) fixed point or to be of first order.