Universal scaling of conserved charge in the stochastic diffusion dynamics

In this paper, we explore the Kibble-Zurek scaling of the conserved charge, using the stachastic diffusion dynamics. After determining the characteristic scales $\tau_{kz}$ and $l_{kz}$ and properly rescaling the traditional correlation function and cumulant, we construct universal functions for both the two-point correlation function $C(y_1-y_2;\tau)$ and second-order cumulant $K(\Delta y,\tau)$ of the conserved charge in the critical regime, which are insensitive to the initial temperature and a parameter in the mapping between 3D Ising model and the hot QCD system near the critical point.