Universal scaling of conserved charge in stochastic diffusion dynamics

We explore the Kibble-Zurek scaling of conserved charge using stochastic diffusion dynamics. The characteristic scales and are determined and used to properly rescale the traditional correlation function and cumulant. We construct universal functions for the two-point correlation and the second-order cumulant of the conserved charge in the critical regime, both of which are, near the critical point, insensitive to both the initial temperature and a parameter in the mapping between the 3D Ising model and the hot QCD system.