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 [$p_c = 0.7112687(2)$], 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 $\sim t^\gamma$ with $\gamma < 1$), which is easily understood as a consequence of the initial decay of activity, $\rho(t) \sim t^{-\delta}$, with $\gamma = 1- \delta$. We verify that at criticality, the activity correlation function $C(r) \sim r^{-\beta/\nu_\perp}$, 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. 
Sharon Dantas da Cunha, Luciano Rodrigues da Silva, Gandhimohan M.   Viswanathan and Ronald Dickman
cond-mat.stat-mech