Phys. Rev. E 75, 030102(R) (2007) [4 pages]Self-affinity in the gradient percolation problem
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 ∼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. © 2007 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.75.030102
DOI:
10.1103/PhysRevE.75.030102
PACS:
64.60.Ak, 02.50.−r, 05.40.Fb
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