Self-organized branching processes: Avalanche models with dissipation

TL;DR

This paper investigates how dissipation affects self-organized criticality in sandpile models, showing that dissipation drives the system into a subcritical state and alters critical behavior.

Contribution

It generalizes a self-organized branching process to include dissipation, revealing the shift from critical to subcritical states and analyzing the resulting critical exponents.

Findings

Dissipation causes the system to be subcritical rather than critical.

The critical exponents for avalanche size and lifetime are analytically derived.

Numerical studies confirm the analytical predictions.

Abstract

We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the model self-organizes not into a critical state but rather into a subcritical state: when dissipation is present, the dynamical fixed point does not coincide with the critical point. Thus the level of dissipation acts as a relevant parameter in the renormalization-group sense. We study the model numerically and compute analytically the critical exponents for the avalanche size and lifetime distributions and the scaling exponents for the corresponding cutoffs.