Creep dynamics of elastic manifolds via exact transition pathways

Abstract

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

14 pages, 18 figures

References in corpus (40)

• Crackling Noise
• Elastic theory of flux lattices in presence of weak disorder
• Creep and flow regimes of magnetic domain wall motion in ultrathin Pt/Co/Pt films with perpendicular anisotropy
• Statistical Models of Fracture
• Creep and depinning in disordered media
• Strong disorder RG approach of random systems
• Fractional Laplacian in Bounded Domains
• Velocity of domain-wall motion induced by electrical current in a ferromagnetic semiconductor (Ga,Mn)As
• Crackling dynamics in material failure as the signature of a self-organized dynamic phase transition
• 2-loop Functional Renormalization Group Theory of the Depinning Transition
• Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films
• Nonequilibrium Dynamics of Interfaces and Lines
• Two-dimensional scaling properties of experimental fracture surfaces
• Pinning and Sliding of Driven Elastic Systems: from Domain Walls to Charge Density Waves
• Roughness at the depinning threshold for a long-range elastic string
• From Individual to Collective Pinning: Effect of Long-range Elastic Interactions
• Driven Depinning in Anisotropic Media
• Origin of the roughness exponent in elastic strings at the depinning threshold
• Width distribution of contact lines on a disordered substrate
• Dynamics below the depinning threshold
• Creep motion of an elastic string in a random potential
• Avalanches and the Renormalization Group for Pinned Charge-Density Waves
• Thermal rounding of the depinning transition
• Critical exponents of the driven elastic string in a disordered medium
• Universal Statistics of the Critical Depinning Force of Elastic Systems in Random Media
• Ageing memory and glassiness of a driven vortex system
• Creep in One Dimension and Phenomenological Theory of Glass Dynamics
• Non-equilibrium relaxation of an elastic string in a random potential
• Monte Carlo Dynamics of driven Flux Lines in Disordered Media
• Short time relaxation of a driven elastic string in a random medium
• Velocity-force characteristics of a driven interface in a disordered medium
• Functional renormalization group for anisotropic depinning and relation to branching processes
• Interface Motion in Random Media at Finite Temperature
• Scaling of Energy Barriers for Flux Lines and Other Random Systems
• Creep of a fracture line in paper peeling
• Universal depinning force fluctuations of an elastic line: Application to finite temperature behavior
• A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems
• Non-equilibrium dynamics of polymers and interfaces in random media : conjecture $\psi =d_s/2$ for the barrier exponent
• Roughness of a Tilted Anharmonic String at Depinning
• Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?

Cited by in corpus (62)

• Avalanche-size distribution at the depinning transition: A numerical test of the theory
• Universal pinning energy barrier for driven domain walls in thin ferromagnetic films
• Pinning dependent field driven domain wall dynamics and thermal scaling in an ultrathin Pt/Co/Pt magnetic film
• Pinning of Domain Walls in thin Ferromagnetic Films
• Non-steady relaxation and critical exponents at the depinning transition
• Numerical Approaches on Driven Elastic Interfaces in Random Media
• Current-induced viscoelastic topological unwinding of metastable skyrmion strings
• Disordered Elastic Systems and One-Dimensional Interfaces
• Spatio-temporal patterns in ultra-slow domain wall creep dynamics
• Increased lifetime of metastable skyrmions by doping
• Creep motion of elastic interfaces driven in a disordered landscape
• Thermal rounding exponent of the depinning transition of an elastic string in a random medium
• Deformation and flow of amorphous solids: An updated review of mesoscale elastoplastic models
• Magnetic domain wall creep and depinning: a scalar field model approach
• Domain Wall Roughness in Stripe Phase BiFeO${}_3$ Thin Films
• Thermal rounding of the depinning transition in ultrathin Pt/Co/Pt films
• Intermittent collective dynamics of domain walls in the creep regime
• Random-Manifold to Random-Periodic Depinning of an Elastic Interface
• Transient magnetic domain wall AC dynamics by means of MOKE microscopy
• Universal non stationary dynamics at the depinning transition
• Temperature-induced crossovers in the static roughness of a one-dimensional interface
• Creep and thermal rounding close to the elastic depinning threshold
• The elastic depinning transition of vortex lattices in two dimensions
• Common universal behaviors of magnetic domain walls driven by spin-polarized electrical current and magnetic field
• Excess velocity of magnetic domain walls close to the depinning field
• Seismic cycles, size of the largest events, and the avalanche size distribution in a model of seismicity
• On the Dynamics of Glassy Systems
• Maximum relative height of elastic interfaces in random media
• Spatially periodic domain wall pinning potentials: Asymmetric pinning and dipolar biasing
• Strength and length-scale of the interaction between domain walls and pinning disorder in thin ferromagnetic films
• Driven interfaces: from flow to creep through model reduction
• Uniqueness of the thermodynamic limit for driven disordered elastic interfaces
• Universal dimensional crossover of domain wall dynamics in ferromagnetic films
• Instantaneous Normal Modes Reveal Structural Signatures for the Herschel-Bulkley Rheology in Sheared Glasses
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• Pinning time statistics for vortex lines in disordered environments
• Thermally rounded depinning of an elastic interface on a washboard potential
• Effect of disorder geometry on the critical force in disordered elastic systems
• Disordered vortex matter out of equilibrium: a Langevin molecular dynamics study
• Roughening of the anharmonic Larkin model
• Revealing nanoscale disorder in W/CoFeB/MgO ultra-thin films using domain wall motion
• Domain-wall roughness in GdFeCo thin films: crossover length scales and roughness exponents
• On the critical region of long-range depinning transitions
• Creep motion of a domain wall in the two-dimensional random-field Ising model with a driving field
• Model of bound interface dynamics for coupled magnetic domain walls
• Depinning of stiff directed lines in random media
• Earthquake-like dynamics in ultrathin magnetic film
• Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
• Segmental front line dynamics of randomly pinned ferroelastic domain walls
• Tuning Ginzburg-Landau theory to quantitatively study thin ferromagnetic materials
• Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
• Nonsteady dynamic properties of a domain wall for the creep state under an alternating driving field
• Crack propagation by activated avalanches during creep and fatigue from elastic interface theory
• Depinning and flow of a vortex line in an uniaxial random medium
• On mean field theory for ac-driven elastic interfaces exposed to disorder
• Curvature-driven AC-assisted creep dynamics of magnetic domain walls
• Perturbation theory for ac-driven interfaces in random media
• Depinning free of the elastic approximation
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Roughening of the Anharmonic Elastic Interface in Correlated Random Media
• Effect of Ir growth pressure on the domain wall dynamics in Ta/Pt/Co/Ir/Ta stacks
• Field-dependent roughness of moving domain walls in a Pt/Co/Pt magnetic thin film