Dynamic scaling of order parameter fluctuations in model B

We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent z3. 972 (2), which agrees with predictions of the epsilon expansion. We also study nonequilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.