# Critical behavior of plastic depinning of vortex lattices in two dimensions: Molecular dynamics simulations

## TL;DR

This study uses molecular dynamics simulations to analyze the critical behavior of vortex lattice depinning in two dimensions, revealing universal critical exponents and chaotic dynamics at the depinning transition.

## Contribution

It demonstrates that vortex lattice depinning in 2D exhibits second-order critical behavior with universal exponents, supported by scaling analysis and chaos evidence.

## Key findings

- Depinning transition is continuous and critical in strong disorder.
- Critical exponents .75 and 1.3 are universal across disorder types.
- Chaotic dynamics are present throughout the critical region.

## Abstract

Using molecular dynamics simulations, we report a study of the dynamics of two-dimensional vortex lattices driven over a disordered medium. In strong disorder, when topological order is lost, we show that the depinning transition is analogous to a second order critical transition: the velocity-force response at the onset of motion is continuous and characterized by critical exponents. Combining studies at zero and nonzero temperature and using a scaling analysis, two critical expo- nents are evaluated. We find v\sim (F-F_c)^\beta with \beta=1.3\pm0.1 at T=0 and F>F_c, and v\sim T^{1/\delta} with \delta^{-1}=0.75\pm0.1 at F=F_c, where F_c is the critical driving force at which the lattice goes from a pinned state to a sliding one. Both critical exponents and the scaling function are found to exhibit universality with regard to the pinning strength and different disorder realizations. Furthermore, the dynamics is shown to be chaotic in the whole critical region.