Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy
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arXiv
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| Format: | Preprint |
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2024
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| author | Astillero, A. Ruiz-Lorenzo, J. J. |
| author_facet | Astillero, A. Ruiz-Lorenzo, J. J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14275 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy Astillero, A. Ruiz-Lorenzo, J. J. Disordered Systems and Neural Networks Statistical Mechanics 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. |
| title | Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy |
| topic | Disordered Systems and Neural Networks Statistical Mechanics |
| url | https://arxiv.org/abs/2410.14275 |