Depinning and flow of a vortex line in a uniaxial random medium

ELÍAS, FEDERICO; JÖRG WIESE, KAY; KOLTON, ALEJANDRO B.

PHYSICAL REVIEW B

AMER PHYSICAL SOC

Lugar: New York; Año: 2022 vol. 105

1098-0121

We study numerically and analytically the dynamics of a single directed elastic string driven through a three-dimensional disordered medium. In the quasistatic limit the string is super-rough in the direction of the driving force, with roughness exponent ζ = 1.25 ± 0.01, dynamic exponent z = 1.43 ± 0.01, correlation-length exponent ν = 1.33 ± 0.02, depinning exponent β = 0.24 ± 0.01, and avalanche-size exponent τ =1.09 ± 0.03. In the transverse direction we find ζ ⊥ = 0.5 ± 0.01, z ⊥ = 2.27 ± 0.05, and τ ⊥ = 1.17 ± 0.06. Our results show that transverse fluctuations do not alter the critical exponents in the driving direction, as predicted by the planar approximation (PA) proposed by Ertas and Kardar (EK) [Phys. Rev. B 53, 3520 (1996)]. We check the PA for the measured force-force correlator, comparing to the functional renormalization- group and numerical simulations. Both random-bond (RB) and random-field (RF) disorder yield a single universality class, indistinguishable from the one of an elastic string in a two-dimensional random medium. While relations z ⊥ = z + 1/ν and ν = 1/(2 − ζ ) of EK are satisfied, the transversal movement is that of a Brownian, with a clock set locally by the forward movement. This implies ζ ⊥ = (2 − d )/2, distinct from EK. Finally, at small driving velocities the distribution of local parallel displacements has a negative skewness,while in the transverse direction it is a Gaussian. For large scales, the system can be described by anisotropic effective temperatures defined from generalized fluctuation-dissipation relations. In the fast-flow regime the local displacement distributions become Gaussian in both directions and the effective temperatures vanish as⊥⊥∼ 1/v and T eff∼ 1/v 3 for RB disorder and as T eff≈ T eff∼ 1/v for RF disorder.