Self-organisation to criticality in a system without conservation law

TL;DR

This paper studies how the nonconservative OFC earthquake model self-organizes to a critical state, revealing boundary-driven dynamics, a universal critical exponent, and the scaling of transient times with system size.

Contribution

It demonstrates that the OFC model's self-organization process is boundary-driven and governed by a universal dynamical critical exponent, with transient times scaling as system size to the power of z.

Findings

Self-organization initiates from system boundaries.

A universal critical exponent z~1.3 governs dynamics.

Transient time scales as L^z, indicating long-range correlations.

Abstract

We numerically investigate the approach to the stationary state in the nonconservative Olami-Feder-Christensen (OFC) model for earthquakes. Starting from initially random configurations, we monitor the average earthquake size in different portions of the system as a function of time (the time is defined as the input energy per site in the system). We find that the process of self-organisation develops from the boundaries of the system and it is controlled by a dynamical critical exponent z~1.3 that appears to be universal over a range of dissipation levels of the local dynamics. We show moreover that the transient time of the system $t_{tr}$ scales with system size L as $t_{tr} \sim L^z$. We argue that the (non-trivial) scaling of the transient time in the OFC model is associated to the establishment of long-range spatial correlations in the steady state.