Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile

We perform large-scale simulations of a two-dimensional restricted height conserved stochastic sandpile, focusing on particle diffusion and mobility, and spatial correlations. Quasistationary (QS) simulations yield the critical particle density to high precision [pc = 0.7112687(2)], and show that the diffusion constant scales in the same manner as the activity density, as found previously in the one-dimensional case. Short-time scaling is characterized by subdiffusive behavior (mean-square displacement ~ tγ with γ < 1), which is easily understood as a consequence of the initial decay of activity, ρ(t) ~ t−δ, with γ = 1 − δ. We verify that at criticality, the activity-activity correlation function , as expected at an absorbing-state phase transition. Our results for critical exponents are consistent with, and somewhat more precise than, predictions derived from the Langevin equation for stochastic sandpiles in two dimensions.