Universal distribution of threshold forces at the depinning transition

TL;DR

This paper analyzes the universal distribution of threshold forces at the depinning transition in disordered elastic systems, using FRG techniques to reveal universal behavior characterized by just two parameters.

Contribution

It provides a theoretical computation of the force distribution at depinning, demonstrating its universality and comparing it with recent numerical simulations.

Findings

Distribution is universal up to two parameters

Distribution characterized by average critical force and width

Results align with recent numerical simulations

Abstract

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.