Universal Nonstationary Dynamics at the Depinning Transition

2009/06/13 by Alejandro B. Kolton, Grégory Schehr, Gregory Schehr +1 · 26 citations
Mathematics · Physics and Astronomy · #Condensed matter physics #Critical exponent #Crossover #Domain (mathematical analysis) #Dynamics (music) #Exponent #Ferromagnetism #Mathematical analysis #Mathematical physics #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Relaxation (psychology) #Renormalization group #Scaling #Statistical physics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1103/physrevlett.103.160602

published in Physical Review Letters 103(16), 160602 (American Physical Society) · 4 pages, 3 figures

arxiv created 2009/06/13 · openalex publication_date 2009/10/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the nonstationary 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 nonsteady driven dynamics of domain walls in ferromagnetic films and contact lines in wetting.

Citations

• Critical exponents of the driven elastic string in a disordered medium
• Short-time relaxation of a driven elastic string in a random medium
• Exact multilocal renormalization of the effective action: Application to the random sine Gordon model statics and nonequilibrium dynamics
• Dynamics below the Depinning Threshold in Disordered Elastic Systems
• Functional renormalization for pinned elastic systems away from their steady states
• Renormalization of Pinned Elastic Systems: How Does It Work Beyond One Loop?
• Monte Carlo dynamics of driven elastic strings in disordered media
• Two-loop functional renormalization group theory of the depinning transition