Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media

TL;DR

This paper investigates the universal statistical behavior of the critical depinning force in elastic systems within random media, revealing Gaussian and Gumbel distribution regimes linked to the system's periodicity and disorder.

Contribution

It uncovers the connection between depinning transition properties and extreme value statistics, establishing universal distribution functions for different elastic systems.

Findings

Gaussian distribution for periodic systems

Universal functions from Gaussian to Gumbel for random manifolds

Distributions are experimentally accessible in macroscopic systems

Abstract

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.