Mean-field avalanches in jammed spheres

TL;DR

This paper develops a probabilistic approach to analyze avalanches in mean-field disordered systems, revealing conditions for power-law distributions and validating predictions with simulations of jammed spheres.

Contribution

It introduces a novel probabilistic method to compute avalanche distributions in mean-field models with replica symmetry breaking, linking theory with simulation results.

Findings

Power-law behavior in avalanche distributions under certain conditions

Agreement between theoretical predictions and 3D sphere simulations

Identification of conditions leading to scale-invariant avalanches

Abstract

Disordered systems are characterized by the existence of many sample- dependent local energy minima, that cause a stepwise response when the system is perturbed. In this article we use an approach based on elementary probabilistic methods to compute the complete probability distribution of the jumps (static avalanches) in the response of mean-field systems described by replica symmetry breaking; we find a precise condition for having a power-law behavior in the distribution of avalanches caused by small perturbations, and we show that our predictions are in remarkable agreement both with previous results and with what is found in simulations of three dimensional systems of soft-spheres, either at jamming or at slightly higher densities.