On criticality of interface depinning and origin of "bump" in the avalanche distribution

TL;DR

This paper investigates the critical behavior of interface depinning transitions, revealing how initial conditions influence avalanche distributions and explaining the origin of the characteristic "bump" in size distributions.

Contribution

It demonstrates that variations in initial interface height and curvature lead to distinct avalanche populations, clarifying the origin of the bump in the distribution.

Findings

Avalanches can be categorized into subcritical, critical, and supercritical groups.

The interface height distribution asymmetry causes an excess of supercritical avalanches.

The bump in the avalanche size distribution is due to the mixture of different avalanche populations.

Abstract

The depinning transition critical point is manifested as power-law distributed avalanches exhibited by slowly driven elastic interfaces in quenched random media. Here we show that since avalanches with different starting heights relative to the mean interface height or different initial local interface curvatures experience different excess driving forces due to elasticity, avalanches close to the "global" critical point of non-mean field systems can be separated into populations of subcritical, critical and supercritical ones. The asymmetric interface height distribution results in an excess of supercritical avalanches, manifested as a "bump" in the avalanche size distribution cutoff.