Universal scaling of non-equilibrium critical fluctuations from Langevin dynamics of model A

TL;DR

This paper demonstrates the universal scaling behavior of non-equilibrium critical fluctuations in Langevin dynamics of model A, using the Kibble-Zurek mechanism to identify scale-invariant functions near the critical point.

Contribution

It introduces a universal scaling framework for non-equilibrium critical fluctuations based on Langevin dynamics and the Kibble-Zurek mechanism, independent of non-universal factors.

Findings

Universal functions for cumulants show scale-invariance near critical point

Scaling functions are independent of relaxation time and evolution trajectory

Provides a framework for analyzing non-equilibrium critical phenomena

Abstract

Within the framework of the Kibble-Zurek Mechanism, we investigate the universal behavior of the non-equilibrium critical fluctuations, using the Langevin dynamics of model A. With properly located typical time, length and angle scales, $\tau_{\mbox{KZ}}$, $l_{\mbox{KZ}}$, and $\theta_{\mbox{KZ}}$, the constructed functions $\bar{f}_n((\tau-\tau_c)/\tau_{\mbox{KZ}},\theta_{\mbox{KZ}})$ (n=1...4) for the cumulants of the sigma field show universal behavior near the critical point, which are independent from some non-universal factors, such as the relaxation time or the evolution trajectory.