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

A. Astillero1,2 and J. J. Ruiz-Lorenzo3,2

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Phys. Rev. E 111, 064126 – Published 20 June, 2025

DOI: https://doi.org/10.1103/q72t-1xw7

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 on the study of the dynamic correlation length, allowing 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.

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Phys. Rev. E 111, 064126– Published 20 June, 2025
  • Received 25 October 2024
  • Revised 29 May 2025
  • Accepted 5 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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