Brain, Rain and Forest Fires -- What is critical about criticality: In praise of the correlation function

TL;DR

This paper reviews how power laws and correlation functions serve as indicators of criticality across diverse systems like rain, brain activity, and forest fires, emphasizing shared self-organization near critical states.

Contribution

It compares phenomenology from different systems to highlight common features of self-organization and criticality, emphasizing the role of correlation functions and power laws.

Findings

Shared extended correlations across systems

Power laws indicative of criticality in diverse phenomena

Self-organization near critical states

Abstract

We present a brief review of power laws and correlation functions as measures of criticality and the relation between them. By comparing phenomenology from rain, brain and the forest fire model we discuss the relevant features of self-organisation to the vicinity about a critical state. We conclude that organisation to a region of extended correlations and approximate power laws may be behaviour of interest shared between the three considered systems.