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

Abstract

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 [$p_c = 0.7112687(2)$], 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 $\sim t^γ$ with $γ< 1$), which is easily understood as a consequence of the initial decay of activity, $ρ(t) \sim t^{-δ}$, with $γ= 1- δ$. We verify that at criticality, the activity correlation function $C(r) \sim r^{-β/ν_\perp}$, 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.