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

TL;DR

This study uses large-scale simulations to analyze particle diffusion, activity, and correlations in a two-dimensional conserved stochastic sandpile, providing precise critical parameters and confirming theoretical predictions.

Contribution

It offers high-precision estimates of the critical particle density and critical exponents, extending understanding from one-dimensional to two-dimensional stochastic sandpiles.

Findings

Critical particle density $p_c = 0.7112687(2)$

Diffusion constant scales with activity density

Subdiffusive behavior observed at short times

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.