Chiral transitions in three-dimensional magnets and higher order \epsilon-expansion

TL;DR

This paper investigates the critical behavior of three-dimensional helimagnets and antiferromagnets using advanced -expansion techniques, concluding that continuous chiral transitions are unlikely in certain spin systems.

Contribution

It provides a three-loop -expansion analysis of chiral transitions, offering new numerical estimates that challenge previous assumptions about the nature of these phase transitions.

Findings

Continuous chiral transitions are ruled out for Heisenberg or planar spins.

Numerical estimates of marginal order parameter dimensionality N.

Analysis based on resummation of -expansions.

Abstract

The critical behaviour of helimagnets and stacked triangular antiferromagnets is analyzed in (4 - \epsilon) dimensions within three-loop approximation. Numerical estimates for marginal values of the order parameter dimensionality N obtained by resummation of corresponding \epsilon-expansions rule out the possibility of continuous chiral transitions in magnets with Heisenberg or planar spins.