Sequential disruption of the shortest path in critical percolation.

Abstract

We investigate the effect of sequentially disrupting the shortest path of percolation clusters at criticality by comparing it with the shortest alternative path. We measure the difference in length and the enclosed area between the two paths. The sequential approach allows us to study spatial correlations. We find the lengths of the segments of successively constant differences in length to be uncorrelated. Simultaneously, we study the distance between red bonds. We find the probability distributions for the enclosed areas A, the differences in length Δl, and the lengths between the red bonds l_{r} to follow power-law distributions. Using maximum likelihood estimation and extrapolation we find the exponents β=1.38±0.03 for Δl, α=1.186±0.008 for A, and δ=1.64±0.03 for the distribution of l_{r}.