Monte Carlo study of the ordering of the weakly anisotropic Heisenberg spin glass in magnetic fields

TL;DR

This study uses Monte Carlo simulations to investigate the phase transitions in a weakly anisotropic Heisenberg spin glass under magnetic fields, revealing a chiral replica symmetry breaking transition and emphasizing the role of chirality.

Contribution

It provides the first extensive numerical evidence for a chiral replica symmetry breaking transition in the weakly anisotropic Heisenberg spin glass, supporting the spin-chirality decoupling-recoupling scenario.

Findings

Chiral RSB transition occurs alongside spin-glass order.

The phase diagram resembles experimental observations.

Chirality plays a crucial role in spin-glass ordering.

Abstract

The ordering of the three-dimensional Heisenberg spin glass with the weak random anisotropy in magnetic fields is studied by extensive equilibrium Monte Carlo simulations. Both the spin and the chirality are monitored. We find strong numerical evidence that a replica symmetry breaking transition occurs in the chiral sector, which accompanies the simultaneous spin-glass order. Despite the similarity in the global symmetry, the ordering behavior of the weakly anisotropic Heisenberg spin glass differs significantly from that of the strongly anisotropic Ising spin glass. The obtained phase diagram in the temperature - magnetic field plane is similar to the experimental phase diagram. Our results highlight the importance of the chirality in the spin-glass ordering of the Heisenberg-like spin glass, and support the spin-chirality decoupling-recoupling scenario of spin-glass transitions.