Self-Affinity in the Gradient Percolation Problem

Details Self-Affinity in the Gradient Percolation Problem Self-Affinity in the Gradient Percolation Problem

2005-11-22

arxiv.org/abs/cond-mat/0511545v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures

Scientific paper

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 2/3 up to a cutoff-length proportional to the gradient to the power (-4/7). 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 multi affinity, is due to the dominance of overhangs at small distances in the structure function. This is a crossover effect.

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