Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems

Details Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems Fractal Behavior of the Shortest Path Between Two Lines in Percolation Systems

2002-03-05

arxiv.org/abs/cond-mat/0203092v1

Physics

Condensed Matter

Statistical Mechanics

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Scientific paper

10.1103/PhysRevE.65.066105

Using Monte-Carlo simulations, we determine the scaling form for the probability distribution of the shortest path, $\ell$, between two lines in a 3-dimensional percolation system at criticality; the two lines can have arbitrary positions, orientations and lengths. We find that the probability distributions can exhibit up to four distinct power law regimes (separated by cross-over regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.

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