Sequential disruption of the shortest path in critical percolation

Abstract

We investigate the effect of sequentiallydisrupting 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 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 $\Delta l$, and the lengths between the redbonds $l_r$ to follow power law distributions. Using maximum likelihood estimation and extrapolation we find the exponents $\beta$ = 1.38 $\pm$ 0.03 for $\Delta l$, $\alpha$ = 1.186 $\pm$ 0.008 for A and $\delta$ = 1.64 $\pm$ 0.025 for thedistribution of $l_r$.