Depinning free of the elastic approximation

Alejandro B. Kolton, Ezequiel E. Ferrero, Alberto Rosso
Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech)
Phys. Rev. B 108, 174201 (2023)
2023-06-22 16:00:00
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.
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