Universal scaling of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>σ</mml:mi></mml:math> field and net-protons from Langevin dynamics of model A

Abstract

In this paper, we investigate the Kibble-Zurek scaling of the $\ensuremath{\sigma}$ field and net-protons within the framework of Langevin dynamics of model A. After determining the characteristic scales ${\ensuremath{\tau}}_{\text{KZ}},{l}_{\text{KZ}}$, and ${\ensuremath{\theta}}_{\text{KZ}}$ and properly rescaling the traditional cumulants, we construct universal functions for the $\ensuremath{\sigma}$ field and approximate universal functions for net-protons in the critical regime, which are insensitive to the relaxation time and the chosen evolving trajectory. Besides, the oscillating behavior for the higher order cumulants of net-protons near the critical point is also drastically suppressed, which converge into approximate universal curves with these constructed Kibble-Zurek functions.