Depinning exponents of the driven long-range elastic string

2006/12/31 by Olaf Duemmer, Werner Krauth
Materials Science · Physics and Astronomy · #Critical exponent #Material Dynamics and Properties #Percolation critical exponents #Physics of Superconductivity and Magnetism #Scaling #String (physics) #Theoretical and Computational Physics #Widom scaling #Zero (linguistics) #cond-mat.dis-nn

paper · pdf · doi:10.1088/1742-5468/2007/01/p01019

published as J. Stat. Mech. (2007) P01019 · 6 pages, 5 figures

openalex publication_date 2007/01/29 · arxiv created 2007/01/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations avoid finite-size effects and improve accuracy. We explicitly demonstrate the equivalence of fixed-velocity and fixed-driving-force simulations. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.

Citations

• Critical exponents of the driven elastic string in a disordered medium
• From individual to collective pinning: Effect of long-range elastic interactions
• Short-time relaxation of a driven elastic string in a random medium
• Non-equilibrium critical phenomena and phase transitions into absorbing 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