Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

TL;DR

This study uses computer simulations of a lattice model to explore how complex relaxation phenomena exhibit apparent scale invariance due to aggregated exponential relaxations, challenging the criticality interpretation.

Contribution

It demonstrates that scale invariance in nonequilibrium relaxation can arise from summing exponential processes, not necessarily from critical phenomena.

Findings

Relaxation occurs via avalanches with multiple scales.

Scale invariance results from summing exponential relaxations.

No evidence supports criticality as the cause of scale invariance.

Abstract

We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a way that closely resembles the relaxation in a large number of complex systems in nature. Such apparent scale invariance simply results in the model from summing over many exponential relaxations, each with a scale which is determined by the curvature of the domain wall at which the avalanche originates. The claim that scale invariance in a nonequilibrium setting is to be associated with criticality is therefore not supported. Some hints that may help in checking this experimentally are discussed.