Self-organized criticality and directed percolation

TL;DR

This paper investigates a stochastic sandpile model, analyzing its phase diagram and critical behavior, revealing a distinct universality class due to boundary conditions and conservation laws, supported by numerical simulations.

Contribution

It introduces a simple sandpile model that captures the key differences between self-organized criticality and directed percolation, highlighting the role of boundary conditions and conservation laws.

Findings

The model exhibits a critical state extended to a line segment due to self-organization.

It has a different universality class from directed percolation because of boundary conditions and conservation laws.

Numerical simulations confirm the theoretical analysis in one dimension.

Abstract

A sandpile model with stochastic toppling rule is studied. The control parameters and the phase diagram are determined through a MF approach, the subcritical and critical regions are analyzed. The model is found to have some similarities with directed percolation, but the existence of different boundary conditions and conservation law leads to a different universality class, where the critical state is extended to a line segment due to self-organization. These results are supported with numerical simulations in one dimension. The present model constitute a simple model which capture the essential difference between ordinary nonequilibrium critical phenomena, like DP, and self-organized criticality.