Gabay-Toulouse Phase Transition in Heisenberg Spin-Glasses in Three Dimensions

TL;DR

This paper investigates phase transitions in three-dimensional Heisenberg spin glasses, finding evidence for a Gabay-Toulouse transition without anisotropies and no transition when anisotropies are present, challenging previous chirality-based theories.

Contribution

It provides new computational evidence for the Gabay-Toulouse transition in Heisenberg spin glasses without anisotropies, contrasting with prior chirality scenario predictions.

Findings

Gabay-Toulouse transition occurs without anisotropies.

No phase transition when anisotropies are present.

Calculated stiffness exponents and correlation lengths support these results.

Abstract

We examine three-dimensional $\pm J$ Heisenberg models with and without random anisotropies in a magnetic field. We calculate both the stiffness exponent $\theta_s$ at absolute zero temperature and spin-glass correlation lengths for the longitudinal and transverse spin components at finite temperatures. We suggest that, contrary to a chirality scenario predicted by Kawamura and his co-workers, a Gabay-Toulouse phase transition occurs when the anisotropies are absent, although no phase transition occurs when they are present.