Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

Abstract

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Delta(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.

4 pages, 6 figures

References in corpus (20)

• Elastic theory of flux lattices in presence of weak disorder
• Creep and depinning in disordered media
• Collective Transport: From Superconductors to Earthquakes
• Statistics of Earthquakes in Simple Models of Heterogeneous Faults
• 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
• 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
• Depinning of elastic manifolds
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Width distribution of contact lines on a disordered substrate
• Dynamics below the depinning threshold
• Depinning transition of dislocation assemblies: pileup and low-angle grain boundary
• Critical exponents of the driven elastic string in a disordered medium
• Measuring functional renormalization group fixed-point functions for pinned manifolds
• Transport properties of BSCCO crystals with and without surface barriers
• Short time relaxation of a driven elastic string in a random medium
• Interface Motion in Random Media at Finite Temperature

Cited by in corpus (58)

• Avalanche-size distribution at the depinning transition: A numerical test of the theory
• Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of records
• Size distributions of shocks and static avalanches from the Functional Renormalization Group
• Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
• Statistics of static avalanches in a random pinning landscape
• The mechanisms of spatial and temporal earthquake clustering
• Local dynamics of a randomly pinned crack front during creep and forced propagation: An experimental study
• Non-steady relaxation and critical exponents at the depinning transition
• Thermal rounding of the depinning transition
• Avalanche dynamics of elastic interfaces
• An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random media
• Theory and simulations on strong pinning of vortex lines by nanoparticles
• Numerical Approaches on Driven Elastic Interfaces in Random Media
• Distribution of velocities in an avalanche
• From depinning transition to plastic yielding of amorphous media: A soft modes perspective
• Depinning transition for a screw dislocation in a model solid solution
• From microstructural features to effective toughness in disordered brittle solids
• Avalanche Spatial Structure and Multivariable Scaling Functions; Sizes, Heights, Widths, and Views through Windows
• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Cusps and shocks in the renormalized potential of glassy random manifolds: How Functional Renormalization Group and Replica Symmetry Breaking fit together
• Crossover behavior in interface depinning
• Domain Wall Roughness in Stripe Phase BiFeO${}_3$ Thin Films
• Random-Manifold to Random-Periodic Depinning of an Elastic Interface
• Cusps, self-organization, and absorbing states
• Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems
• Crack-front model for adhesion of soft elastic spheres with chemical heterogeneity
• Uniqueness of the thermodynamic limit for driven disordered elastic interfaces
• Field theory of disordered systems -- Avalanches of an elastic interface in a random medium
• The Spatial Shape of Avalanches
• Universal Force Correlations in an RNA-DNA Unzipping Experiment
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: Critical Exponents and Scaling Functions
• Mean-Field Theories for Depinning and their Experimental Signatures
• Interference in disordered systems: A particle in a complex random landscape
• Thermally rounded depinning of an elastic interface on a washboard potential
• Depinning exponents of thin film domain walls depend on disorder strength
• On the critical region of long-range depinning transitions
• Field Theory of Disordered Elastic Interfaces at 3-Loop Order: The $\beta$-Function
• A numerical study of the statistics of roughness parameters for fluctuating interfaces
• Benchmarking the nonperturbative functional renormalization group approach on the random elastic manifold model in and out of equilibrium
• Viscoelastic Interfaces Driven in Disordered Media and Applications to Friction
• Correlations between avalanches in the depinning dynamics of elastic interfaces
• Depinning of stiff directed lines in random media
• Magnetoelectric correlations in BiMnO${}_3$ whithin Landau theory: comparison with experiment
• Non-Gaussian effects and multifractality in the Bragg glass
• Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
• Long-range interactions in the avalanches of elastic interfaces
• Distribution of velocities in an avalanche, and related quantities: Theory and numerical verification
• Roughness and critical force for depinning at 3-loop order
• Dynamical Selection of Critical Exponents
• Stick-slip in a stack: how slip dissonance reveals aging
• Analytical Methods and Field Theory for Disordered Systems
• Depinning and flow of a vortex line in an uniaxial random medium
• Depinning of a discrete elastic string from a two dimensional random array of weak pinning points
• Depinning free of the elastic approximation
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
• Force-Force Correlator for Driven Disordered Systems at Finite Temperature
• Large Orders and Strong-Coupling Limit in Functional Renormalization
• Estimating predictability of depinning dynamics by machine learning