Avalanches and Correlations in Driven Interface Depinning

TL;DR

This paper investigates the critical behavior of driven interfaces in disordered media, revealing modified scaling laws, defining avalanches with a specific dynamical exponent, and identifying a power-law distribution of avalanche sizes.

Contribution

It introduces a new approach to separate local and global dynamics in interface depinning, and relates the behavior to directed percolation and avalanche statistics.

Findings

Dynamical scaling requires modification due to local and global growth interplay.

Defined avalanches with a dynamical exponent z_{loc} approximately 1.63.

Avalanche size distribution follows a power-law with exponent approximately 1.25.

Abstract

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. {\bf 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 $z_{loc} = 1 + \zeta_c \simeq 1.63$ where $\zeta_c$ is the roughness exponent of the interface. We observe that the avalanche size distribution obeys a power-law decay with an exponent $\kappa \simeq 1.25$.