Non-steady relaxation and critical exponents at the depinning transition

Ezequiel E. Ferrero, Sebastian Bustingorry, Alejandro B. Kolton
CONICET, Centro Atomico Bariloche, 8400 San Carlos de Bariloche, Rio Negro, Argentina
arXiv:1211.7275 [cond-mat.stat-mech] (30 Nov 2012)


   author={Ferrero}, E.~E. and {Bustingorry}, S. and {Kolton}, A.~B.},

   title={"{Non-steady relaxation and critical exponents at the depinning transition}"},

   journal={ArXiv e-prints},




   keywords={Condensed Matter – Statistical Mechanics},




   adsnote={Provided by the SAO/NASA Astrophysics Data System}


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We study the non-steady relaxation of a driven one-dimensional elastic interface at the depinning transition by extensive numerical simulations concurrently implemented on graphics processing units (GPUs). We compute the time-dependent velocity and roughness as the interface relaxes from a flat initial configuration at the thermodynamic random-manifold critical force. Above a first, non-universal microscopic time-regime, we find a non-trivial long crossover towards the non-steady macroscopic critical regime. This "mesoscopic" time-regime is robust under changes of the microscopic disorder including its random-bond or random-field character, and can be fairly described as power-law corrections to the asymptotic scaling forms yielding the true critical exponents. In order to avoid fitting effective exponents with a systematic bias we implement a practical criterion of consistency and perform large-scale (L~2^{25}) simulations for the non-steady dynamics of the continuum displacement quenched Edwards Wilkinson equation, getting accurate and consistent depinning exponents for this class: beta=0.245 pm 0.006, z=1.433 pm 0.007, zeta=1.250 pm 0.005 and nu=1.333 pm 0.007. Our study may explain numerical discrepancies (as large as 30% for the velocity exponent beta) found in the literature. It might be also relevant for the analysis of experimental protocols with driven interfaces keeping a long-term memory of the initial condition.
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