Depinning transitions in elastic strings

TL;DR

This paper investigates the depinning transitions of elastic strings in disordered media through two models with different elastic force characteristics, estimating critical points and exponents, and finding they do not belong to known universality classes.

Contribution

It introduces and analyzes two models of elastic string depinning with different elastic forces, estimating critical points and exponents, and demonstrating they form new universality classes.

Findings

Critical points are estimated for both models.

Critical exponents are numerically determined.

Scaling relations are confirmed to hold.

Abstract

We study the depinning transitions of elastic strings in disordered media in two different cases. We consider the elastic forces to be of infinite range in one case, where the magnitude is proportional to the extension of the string. The critical points and elastic behavior can be estimated to some extent in this case. The exponents are estimated numerically and scaling relations are found to be obeyed. We have also considered a model where the elastic force is constant in magnitude. The critical points can again be argued and the critical exponents are numerically estimated. The scaling relations are well obeyed. Both of these models do not fall into known universality classes.