Creep and depinning in disordered media

Abstract

Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive f . We derive functional renormalization group equations which allow to describe in details the properties of the slowly moving states in both cases. Since they hold at finite velocity v, they allow to remedy some shortcomings of the previous approaches to zero temperature depinning. In particular, they enable us to derive the depinning law directly from the equation of motion, with no artificial prescription or additional physical assumptions, such as a scaling relation among the exponents. Our approach provides a controlled framework to establish under which conditions the depinning regime is universal. It explicitly demonstrates that the random potential seen by a moving extended system evolves at large scale to a random field and yields a self-contained picture for the size of the avalanches associated with the deterministic motion. At finite temperature T > 0 we find that the effective barriers grow with lenghtscale as the energy differences between neighboring metastable states, and demonstrate the resulting activated creep law v ∼ exp −C f −µ /T where the exponent µ is obtained in a ǫ = 4 − D expansion (D is the internal dimension of the interface). Our approach also provides quantitatively a new scenario for creep motion as it allows to identify several intermediate lengthscales. In particular, we unveil a novel "depinning-like" regime at scales larger than the activation scale, with avalanches spreading from the thermal nucleus scale up to the much larger correlation length RV . We predict that RV ∼ T −σ f −λ diverges at small drive and temperature with exponents σ, λ that we determine.

Universal distribution of threshold forces at the depinning transition

“…A numerical study in Ref. [22] of the distribution of barriers confirms that the typical barrier scales as the energy minima, as predicted by 1-loop FRG studies [23]. The more difficult question of predicting the distribution of energy barriers was addressed in Ref.…”

“…(6) the renormalized disorder correlator acquires in the vicinity of the fixed-point a scale dependence. Integration over scales beyond the Larkin scale yields (see Ref [23,39] for details):…”

Universality classes and crossover scaling of Barkhausen noise in thin films

“…It would instead be necessary to perform a functional renormalization-group calculation along the lines of Refs. [27][28][29][30][31][32], taking into account explicitly the nonconvex nature of the interaction kernel, leading to a violation of the no-passing rule usually obeyed by depinning interfaces [21].…”

Deblocking of interacting particle assemblies: from pinning to jamming

“…In most situations, however, interactions between particles should be explicitly taken into account. In this case we will still observe a depinning transition, but its quantitative and qualitative features will change [52][53][54][55][56][57][58]. It is convenient to first study an interacting particle system in the elastic approximation, in which the pinning forces are not strong enough to break the topological properties of the particle system.…”

“…These elastic equations are still impossible to solve exactly, but several results have been obtained using scaling theories and renormalization group calculations [52][53][54][55][56][57][58]. In the case of long-range interactions the gradients are replaced by a non-local interaction kernel and the equation becomes…”