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 exponents are evaluated. We find v ∼ (F − Fc) β with β = 1.3 ± 0.1 at T = 0 and F > Fc, and v ∼ T 1/δ with δ −1 = 0.75 ± 0.1 at F = Fc, where Fc 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.

Large-scale numerical simulations are used to study the elastic dynamics of two-dimensional vortex lattices driven on a disordered medium in the case of weak disorder. We investigate the so-called elastic depinning transition by decreasing the driving force from the elastic dynamical regime to the state pinned by the quenched disorder. Similarly to the plastic depinning transition, we find results compatible with a second-order phase transition, although both depinning transitions are very different from many viewpoints. We evaluate three critical exponents of the elastic depinning transition. β = 0.29 ± 0.03 is found for the velocity exponent at zero temperature, and from the velocity-temperature curves we extract the critical exponent δ −1 = 0.28 ± 0.05. Furthermore, in contrast with charge-density waves, a finite-size scaling analysis suggests the existence of a unique diverging length at the depinning threshold with an exponent ν = 1.04 ± 0.04, which controls the critical force distribution, the finite-size crossover force distribution and the intrinsic correlation length. Finally, a scaling relation is found between velocity and temperature with the β and δ critical exponents both independent with regard to pinning strength and disorder realizations.

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