Fractal behavior of the shortest path between two lines in percolation systems.
Using Monte Carlo simulations, we determine the scaling form for the probability distribution of the shortest path l between two lines in a three-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 crossover regimes) with exponents depending on the relative orientations of the lines. We explain this rich fractal behavior with scaling arguments.
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA.
Gerald
G
Paul
Shlomo
S
Havlin
H Eugene
HE
Stanley