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 $\sim t^{\gamma }$ 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.

14 pages; 18 figures

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• Hydrodynamics, density fluctuations and universality in conserved stochastic sandpiles
• Universality of continuous phase transitions on random Voronoi graphs