On the robustness of scale invariance in SOC models

TL;DR

This paper introduces a random neighbor extremal stick-slip model demonstrating that approximate scale invariance occurs over a large critical region, providing insights into the widespread presence of scale invariance in natural systems.

Contribution

The paper presents an analytically solvable extremal model showing how a large critical region can explain the ubiquity of scale invariance in nature.

Findings

Critical point at Jc where the system is exactly critical

Large critical region around Jc with approximate scale invariance

Mean avalanche size is exactly calculable as a function of coupling

Abstract

A random neighbor extremal stick-slip model is introduced. In the thermodynamic limit, the distribution of states has a simple analytical form and the mean avalanche size, as a function of the coupling parameter, is exactly calculable. The system is critical only at a special point Jc in the coupling parameter space. However, the critical region around this point, where approximate scale invariance holds, is very large, suggesting a mechanism for explaining the ubiquity of scale invariance in Nature.