Universal interface width distributions at the depinning threshold

TL;DR

This paper calculates the universal distribution of interface widths at the depinning threshold, confirming universality classes and showing that a generalized Gaussian model effectively describes the distribution across different systems.

Contribution

It introduces a generalized Gaussian framework for interface width distributions at depinning, supported by renormalization analysis and numerical validation.

Findings

Distribution matches universality classes

Generalized Gaussian approximates the distribution well

Universal kurtosis ratio computed and validated

Abstract

We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well approximated by a generalized Gaussian theory of independant modes which decay with a characteristic propagator G(q)=1/q^(d+2 zeta); zeta, the roughness exponent, is computed independently. A functional renormalization analysis explains this result and allows to compute the small deviations, i.e. a universal kurtosis ratio, in agreement with numerics. We stress the importance of the Gaussian theory to interpret numerical data and experiments.