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Diffusion, correlations and mobility in a two-dimensional conserved stochastic sandpile

Sharon Dantas da Cunha 1 ; Ronald Dickman 2
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The conserved stochastic sandpile (CSS) belong to a universality class called {\it conserved directed percolation} (CDP) [1,2,3,4], distinct from directed percolation (DP). The existence of the CDP class was nevertheless questioned by Basu {\it et al.} [5], who claim that the one-dimensional CSS belongs to the DP class, but these results were reexamined in one and two dimensions by Lee [6,7], who presented numerical evidence to prove the existence of CDP. In this work we perform large-scale simulations of a two-dimensional restricted-height conserved stochastic sandpile, focusing on particle diffusion, spatial correlations and mobility. Initially we use Quasistationary simulations (QS) to determine the critical particle density [$p_c = 0.7112687(2)$], and show that the diffusion constant scales in the same manner as the activity density, as found previously in the one-dimensional case [3]. We analyze the particles mean-square displacement (msd) and verify the subdiffusive behavior in the initial (``short-time") scaling regime, and linear, in the stationary regime. At criticality, the activity correlation function behaves as $C(r) \sim r^{-\beta/\nu_\perp}$. Our results for critical exponents are consistent with predictions derived from the Langevin equation for stochastic sandpile in two dimensions [8]. The effect of weak force or bias $f$ were studied in CSS, where we implement the bias by altering the transition probabilities and the results were consistent with theoretical relationships.

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