Abstract
We study the finite-size fluctuations at the depinning transition for a one-dimensional elastic interface of size L displacing in a disordered medium of transverse size M = kLζ with periodic boundary conditions, where ζ is the depinning roughness exponent and k is a finite aspect-ratio parameter. We focus on the crossover from the infinitely narrow (k → 0) to the infinitely wide (k → ∞) medium. We find that at the thermodynamic limit both the value of the critical force and the precise behaviour of the velocity–force characteristics are unique and k-independent. We also show that the finite-size fluctuations of the critical force (bias and variance) as well as the global width of the interface cross over from a power-law to a logarithm as a function of k. Our results are relevant for understanding anisotropic size effects in force-driven and velocity-driven interfaces.
Highlights
Understanding anisotropic finite-size effects in driven condensed matter systems is important for the custom numerical simulation analysis and modeling, and to interpret an increasing amount of experiments performed on relatively small samples with specially devised geometries, where one of the system dimensions can be even comparable to a typical static or dynamical correlation length
We study the finite size fluctuations at the depinning transition for a one-dimensional elastic interface of size L displacing in a disordered medium of transverse size M = kLζ with periodic boundary conditions, where ζ is the depinning roughness exponent and k is a finite aspect ratio parameter
We show that the finite size fluctuations of the critical force as well as the global width of the interface cross over from a power-law to a logarithm as a function of k
Summary
Understanding anisotropic finite-size effects in driven condensed matter systems is important for the custom numerical simulation analysis and modeling, and to interpret an increasing amount of experiments performed on relatively small samples with specially devised geometries, where one of the system dimensions can be even comparable to a typical static or dynamical correlation length. Periodic systems such as planar vortex lattices, charge density waves, or experimental realizations of elastic chains in random media, motivate, through an appropriate mapping, the study of the motion of large interfaces in periodically repeated “narrow” media, i.e. much narrower than the interface width [18,19,20]. Minimal models, such as the paradigmatic quenchedEdwards-Wilkinson equation (QEW) and their close quenched disorder variants [21], were shown to successfully capture experimentally observed universal dynam-
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