A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions

TL;DR

This study uses a renormalization group approach to analyze phase transitions in N-component helimagnets in dimensions close to two, revealing conditions for stable fixed points and the nature of phase transitions.

Contribution

It provides a two-loop order analysis of a nonlinear sigma model for helimagnets in D=2+ε dimensions, identifying stable fixed points and symmetry enlargements.

Findings

Stable fixed point exists for N ≥ 3.

Symmetry enlarges to O(4) at N=3.

Phase transition is either first order or second order with O(4) exponents.

Abstract

We study a non linear sigma model $O(N)\otimes O(2)/O(N-2)\otimes O(2)$ describing the phase transition of N-components helimagnets up to two loop order in $D=2+\epsilon$ dimensions. It is shown that a stable fixed point exists as soon as $N$ is greater than 3 (or equal). In the N=3 case, the symmetry of the system is dynamically enlarged at the fixed point to O(4) We show that the order parameter for Heisenberg helimagnets involves a tensor representation of $O(4)$. We show that for large $N$ and in the neighborhood of two dimensions this nonlinear sigma model describes the same critical theory as the Landau-Ginzburg linear theory. We deduce that there exists a dividing line $N_c (D)$ in the plane $(N, D)$ separating a first-order region containing the Heisenberg point at $D=4$ and a second-order region containing the whole $D=2$ axis. We conclude that the phase transition of Heisenberg helimagnets in dimension 3 is either first order or second order with $O(4)$ exponents involving a tensor representation or tricritical.