Anisotropic Scaling in Depinning of a Flux Line

TL;DR

This paper investigates the depinning transition of flux lines, revealing anisotropic effects that lead to new universality classes, with detailed analysis of fluctuations and critical exponents through analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of anisotropic depinning, highlighting the impact of anisotropy on universality classes and critical behavior of flux lines.

Findings

Longitudinal roughness exponent ζ_∥=1

Relaxation exponent z_∥≈4/3

Transverse fluctuations suppressed with ζ_⊥=1/2 and z_⊥=z_∥+1

Abstract

We study the depinning of a flux line by analytical and numerical methods applied to a phenomenological equation of motion. Transverse fluctuations do not influence the critical behavior of the longitudinal component, justifying ``planar approximations". In an isotropic medium, longitudinal fluctuations have a roughness exponent $\zeta_\parallel=1$, and relax with a dynamic exponent $z_\parallel\approx4/3$; transverse fluctuations are suppressed ($\zeta_\perp=1/2<\zeta_\parallel$), and relax more slowly, with $z_\perp=z_\parallel+1$. Anisotropy in the depinning threshold, or orientational dependence of force-force correlations, lead to new universality classes.