Self-Organized Criticality in the Olami-Feder-Christensen model

TL;DR

This paper investigates the criticality of the Olami-Feder-Christensen model, demonstrating that it is only critical in the conservative regime by analyzing the branching rate sigma rather than relying solely on avalanche size distributions.

Contribution

The study introduces a new method analyzing the branching rate sigma to determine criticality, challenging previous conclusions about the model's behavior.

Findings

The model is critical only in the conservative regime.

Finite-size scaling can be misleading for criticality assessment.

Branching rate analysis provides clearer evidence of criticality.

Abstract

A system is in a self-organized critical state if the distribution of some measured events (avalanche sizes, for instance) obeys a power law for as many decades as it is possible to calculate or measure. The finite-size scaling of this distribution function with the lattice size is usually enough to assume that any cut off will disappear as the lattice size goes to infinity. This approach, however, can lead to misleading conclusions. In this work we analyze the behavior of the branching rate sigma of the events to establish whether a system is in a critical state. We apply this method to the Olami-Feder-Christensen model to obtain evidences that, in contrast to previous results, the model is critical in the conservative regime only.