Correlations in avalanche critical points

TL;DR

This paper investigates correlations in avalanche critical points within the 3D RFIM model, revealing finite correlations between waiting times and avalanche sizes, akin to observations in earthquakes and forest fires, and linking these to critical points at first-order transition ends.

Contribution

It identifies and characterizes a novel correlation in avalanche dynamics within the 3D RFIM, connecting it to real-world phenomena and critical point behavior.

Findings

Finite correlation between waiting intervals and avalanche size in 3D RFIM

Correlation not present in standard BTW model

Correlation observed in earthquakes and forest fires

Abstract

Avalanche dynamics and related power law statistics are ubiquitous in nature, arising in phenomena like earthquakes, forest fires and solar flares. Very interestingly, an analogous behavior is associated with many condensed matter systems, like ferromagnets and martensites. Bearing it in mind, we study the prototypical 3D RFIM at T=0. We find a finite correlation between waiting intervals between avalanches and the previous avalanche size. This correlation is not found in other models for avalanches, such as the standard BTW model, but it is experimentally found in earthquakes and in forest fires. Our study suggests that this effect occurs in critical points which are at the end of an athermal first-order transition line separating two behaviors: one with high activity from another with low activity.