Depinning exponents of the driven long-range elastic string

TL;DR

This paper presents high-precision numerical calculations of critical exponents for a long-range elastic string at the depinning transition, confirming scaling relations and analytical predictions.

Contribution

It provides the first high-precision numerical estimates of depinning exponents for long-range elastic strings, validating theoretical scaling relations.

Findings

Critical exponents are accurately calculated.

Exponents satisfy known scaling relations.

Results agree with analytical predictions.

Abstract

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.