# Critical Scaling and Aging near the Flux Line Depinning Transition

## TL;DR

This study uses Langevin molecular dynamics simulations to analyze the critical behavior and aging phenomena of magnetic flux lines near the depinning transition in type-II superconductors with point defects, identifying critical exponents for different vortex interactions.

## Contribution

It introduces a comprehensive numerical analysis of critical exponents and aging scaling laws for flux lines near depinning, distinguishing between non-interacting and repulsive vortices.

## Key findings

- Numerical critical exponents for flux line depinning identified.
- Scaling laws for gyration radius and velocity established.
- Distinct universality classes for different vortex interactions confirmed.

## Abstract

We utilize Langevin molecular dynamics simulations to study dynamical critical behavior of magnetic flux lines near the depinning transition in type-II superconductors subject to randomly distributed attractive point defects. We employ a coarse-grained elastic line Hamiltonian for the mutually repulsive vortices and purely relaxational kinetics. In order to infer the stationary-state critical exponents for the continuous non-equilibrium depinning transition at zero temperature T = 0 and at the critical driving current density j_c, we explore two-parameter scaling laws for the flux lines' gyration radius and mean velocity as functions of the two relevant scaling fields T and j - j_c. We also investigate critical aging scaling for the two-time height auto-correlation function in the early-time non-equilibrium relaxation regime to independently measure critical exponents. We provide numerical exponent values for the distinct universality classes of non-interacting and repulsive vortices.