Universal non stationary dynamics at the depinning transition

Abstract

We study the non-stationary dynamics of an elastic interface in a disordered medium at the depinning transition. We compute the two-time response and correlation functions, found to be universal and characterized by two independent critical exponents. We find a good agreement between two-loop Functional Renormalization Group calculations and molecular dynamics simulations for the scaling forms, and for the response aging exponent ${\theta }_R$. We also describe a dynamical dimensional crossover, observed at long times in the relaxation of a finite system. Our results are relevant for the non-steady driven dynamics of domain walls in ferromagnetic films and contact lines in wetting.

4 pages, 3 figures

References in corpus (21)

• Creep and flow regimes of magnetic domain wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy
• Statistical Models of Fracture
• Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films
• Creep and depinning in disordered media
• Ageing Properties of Critical Systems
• Renormalization of pinned elastic systems: how does it work beyond one loop ?
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films
• Two-dimensional scaling properties of experimental fracture surfaces
• Depinning of elastic manifolds
• Origin of the roughness exponent in elastic strings at the depinning threshold
• Width distribution of contact lines on a disordered substrate
• Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
• Dynamics below the depinning threshold
• Creep dynamics of elastic manifolds via exact transition pathways
• Critical exponents of the driven elastic string in a disordered medium
• Monte Carlo Dynamics of driven Flux Lines in Disordered Media
• Short time relaxation of a driven elastic string in a random medium
• Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamics
• Functional Renormalization for pinned elastic systems away from their steady states
• Non equilibrium dynamics below the super-roughening transition

Cited by in corpus (17)

• Non-steady relaxation and critical exponents at the depinning transition
• Numerical Approaches on Driven Elastic Interfaces in Random Media
• Thermal quench effects on ferroelectric domain walls
• Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi model
• Thermal rounding exponent of the depinning transition of an elastic string in a random medium
• Excess velocity of magnetic domain walls close to the depinning field
• Dynamic effect of overhangs and islands at the depinning transition in two-dimensional magnets
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Roughening of the anharmonic Larkin model
• Universality class of the depinning transition in the two-dimensional Ising model with quenched disorder
• On the critical region of long-range depinning transitions
• Depinning phase transition in two-dimensional clock model with quenched randomness
• Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
• Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
• On mean field theory for ac-driven elastic interfaces exposed to disorder
• Perturbation theory for ac-driven interfaces in random media
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles