Power-law statistics and universal scaling in the absence of criticality

TL;DR

Power-law statistics and universal scaling can naturally occur in large networks without the system being at criticality, challenging their use as definitive indicators of critical states.

Contribution

This paper demonstrates that power-law and universal scaling features can arise from non-critical, self-sustained regimes in large networks, questioning their role as criticality indicators.

Findings

Power-law statistics emerge in non-critical regimes.

Independent stochastic surrogates replicate observed scaling.

Scaling laws are universal features, not exclusive to criticality.

Abstract

Critical states are sometimes identified experimentally through power-law statistics or universal scaling functions. We show here that such features naturally emerge from networks in self-sustained irregular regimes away from criticality. In these regimes, statistical physics theory of large interacting systems predict a regime where the nodes have independent and identically distributed dynamics. We thus investigated the statistics of a system in which units are replaced by independent stochastic surrogates, and found the same power-law statistics, indicating that these are not sufficient to establish criticality. We rather suggest that these are universal features of large-scale networks when considered macroscopically. These results put caution on the interpretation of scaling laws found in nature.