Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy

TL;DR

This paper investigates the critical dynamics of the 3D Heisenberg model with random cubic anisotropy, estimating the dynamic critical exponent in both equilibrium and out-of-equilibrium regimes, and finds results consistent with theoretical predictions and the 3D site-diluted Ising model.

Contribution

The study provides the first estimates of the dynamic critical exponent for this model in both regimes, confirming theoretical universality class predictions.

Findings

Estimated z=2.50(5) in equilibrium without scaling corrections.

Estimated z=2.29(11) in equilibrium with scaling corrections.

Estimated z=2.38(2) out-of-equilibrium, compatible with equilibrium estimates.

Abstract

We study the critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy in the out-of-equilibrium and equilibrium regimes. Analytical approaches based on field theory predict that the universality class of this model is that of the three-dimensional site-diluted Ising model. We have been able to estimate the dynamic critical exponent by working in the equilibrium regime and by computing the integrated autocorrelation times obtaining $z=2.50(5)$ (without taking into account scaling corrections) and $z=2.29(11)$ (by fixing the scaling corrections to that predicted by field theory). In the out-of-equilibrium regime we have focused in the study of the dynamic correlation length which has allowed us to compute the dynamic critical exponent obtaining $z=2.38(2)$, which is compatible with the equilibrium ones. Finally, both estimates are also compatible with the most accurate prediction $z=2.35(2)$, from numerical simulations of the 3D site-diluted Ising model, in agreement with the predictions based on field theory.