Depinning free of the elastic approximation

TL;DR

This paper models 2D domain-wall depinning using a scalar field, revealing overhangs and crossover behaviors that challenge elastic interface assumptions, and aligns with known universality classes at different scales.

Contribution

It introduces a scalar field model for 2D depinning, capturing overhangs and crossover phenomena, providing a comprehensive picture beyond elastic approximations.

Findings

Critical field scales as Δ^{4/3} for weak disorder.

Overhangs appear beyond a characteristic length l_0, indicating a crossover.

Different universality classes govern behavior below and above l_0.

Abstract

We model the isotropic depinning transition of a domain-wall using a two dimensional Ginzburg-Landau scalar field instead of a directed elastic string in a random media. An exact algorithm accurately targets both the critical depinning field and the critical configuration for each sample. For random bond disorder of weak strength $\Delta$, the critical field scales as $\Delta^{4/3}$ in agreement with the predictions for the quenched Edwards-Wilkinson elastic model. However, critical configurations display overhangs beyond a characteristic length $l_{\tt 0} \sim \Delta^{-\alpha}$, with $\alpha\approx 2.2$, indicating a finite-size crossover. At the large scales, overhangs recover the orientational symmetry which is broken by directed elastic interfaces. We obtain quenched Edwards-Wilkinson exponents below $l_{\tt 0}$ and invasion percolation depinning exponents above $l_{\tt 0}$. A full picture of domain wall isotropic depinning in two dimensions is hence proposed.