1993/08/16 by Heiko Leschhorn, Lei‐Han Tang, Lei-Han Tang · 59 citations
Materials Science · Mathematics · Physics and Astronomy · #Condensed matter physics #Dynamic scaling #Exponent #Geometry #Lattice (music) #Material Dynamics and Properties #Mathematics #Percolation (cognitive psychology) #Physics #Scaling #Statistical physics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat
paper · pdf · doi:10.1103/physreve.49.1238
published in Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 49(2), 1238-1245 (American Physical Society) · 7 pages, (5 figures available upon request), REVTeX, RUB-TP3-93-02
arxiv created 1993/08/16 · openalex publication_date 1994/02/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. 69, 3539 (1992)]. The static and dynamic behavior of the model is related to the properties of directed percolation. We show that, due to the interplay of local and global growth rules, the usual method of dynamical scaling has to be modified. We separate the local from the global part of the dynamics by defining a train of causal growth events, or ``avalanche,'' which can be ascribed a well-defined dynamical exponent zloc=1+\mathrm\ensuremathζc\ensuremath≃1.63, where \mathrm\ensuremathζc is the roughness exponent of the interface.