Out-of-equilibrium scaling corrections and joint universality fit

Develop and implement an out-of-equilibrium fitting methodology that incorporates correction-to-scaling terms and enables a joint fit of datasets for anisotropy strengths D=3 and D=4 to test the universality of the dynamic critical behavior of the three-dimensional Heisenberg model with random cubic anisotropy.

Background

The out-of-equilibrium analysis in this work estimates the dynamic critical exponent from the time dependence of the dynamic correlation length, but the authors note significant statistical correlations in the data at different Monte Carlo times.

Due to these complications, scaling corrections were not included in out-of-equilibrium fits and a joint universality test across D=3 and D=4 could not be performed, leaving a methodological gap to be addressed.

References

The analysis of the out-of-equilibrium data is much more involved (mainly due to the statistical correlations of the data at different Monte Carlo times), and we have not been able to take into account the scaling corrections in the fits and to perform a joint fit for both values of the anisotropy coefficient $D$ (to check universality in the out-of-equilibrium regime).

— Equilibrium and out-of-equilibrium critical dynamics of the three-dimensional Heisenberg model with random cubic anisotropy (2410.14275 - Astillero et al., 18 Oct 2024) in Conclusions