2005/11/30 by Alex Hansen, G. George Batrouni, G. G. Batrouni +3 · 2 citations
Mathematics · Physics and Astronomy · #Markov Chains and Monte Carlo Methods #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.75.030102
4 pages, 4 figures
arxiv created 2006/07/19 · openalex publication_date 2007/03/16 · arxiv updated 2013/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the scaling properties of the solid-on-solid front of the infinite cluster in two-dimensional gradient percolation. We show that such an object is self-affine with a Hurst exponent equal to 23 up to a cutoff length approximately g-4/7, where g is the gradient. Beyond this length scale, the front position has the character of uncorrelated noise. Importantly, the self-affine behavior is robust even after removing local jumps of the front. The previously observed multiaffinity is due to the dominance of overhangs at small distances in the structure function. This is a crossover effect.