title: Self-affinity in the gradient percolation problem.
abstract: 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.
authors.affiliation: Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway. Alex.Hansen@phys.ntnu.no
authors.forename: Alex
authors.initials: A
authors.lastname: Hansen
authors.forename: G George
authors.initials: GG
authors.lastname: Batrouni
authors.forename: Thomas
authors.initials: T
authors.lastname: Ramstad
authors.forename: Jean
authors.initials: J
authors.lastname: Schmittbuhl