2019/06/22 by Oliver Gschwend, Hans J. Herrmann · 2 citations
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Computer science #Distribution (mathematics) #Extrapolation #Mathematical analysis #Mathematics #Path (computing) #Path length #Percolation (cognitive psychology) #Percolation threshold #Physics #Power law #Quantum mechanics #Shortest path problem #Statistical physics #Statistics #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.100.032121
published in Physical review. E 100(3), 032121 (American Physical Society)
arxiv created 2019/06/22 · openalex publication_date 2019/09/16 · arxiv updated 2019/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \mathrm\ensuremathΔl, and the lengths between the red bonds lr to follow power-law distributions. Using maximum likelihood estimation and extrapolation we find the exponents \ensuremathβ=1.38\ifmmode±\else\textpm\fi0.03 for \mathrm\ensuremathΔl, \ensuremathα=1.186\ifmmode±\else\textpm\fi0.008 for A, and \ensuremathδ=1.64\ifmmode±\else\textpm\fi0.03 for the distribution of lr.