Self-organised criticality in stochastic sandpiles: Connection to directed percolation

TL;DR

This paper introduces a stochastic sandpile model demonstrating a crossover from directed percolation to a dissipation-controlled scaling regime, revealing how self-organised criticality emerges through dissipation effects in driven systems.

Contribution

It shows that self-organised criticality in stochastic sandpiles is governed by a dissipation-controlled scaling regime connected to directed percolation, independent of the system's dynamics or dimension.

Findings

System exhibits a crossover from DP to dissipation-controlled scaling.

SOC behaviour is essentially DP modified by dissipation effects.

Demonstrated for both continuous and discrete Manna models.

Abstract

We introduce a stochastic sandpile model where finite drive and dissipation are coupled to the activity field. The absorbing phase transition here, as expected, belongs to the directed percolation (DP) universality class. We focus on the small drive and dissipation limit, i.e. the so-called self-organised critical (SOC) regime and show that the system exhibits a crossover from ordinary DP scaling to a dissipation-controlled scaling which is independent of the underlying dynamics or spatial dimension. The new scaling regime continues all the way to the zero bulk drive limit suggesting that the corresponding SOC behaviour is only DP, modified by the dissipation-controlled scaling. We demonstrate this for the continuous and discrete Manna model driven by noise and bulk dissipation.