2024/11/07 by Mingzhong Lu, Yufeng Song, Lu, Mingzhong +5 · 3 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2411.04748
openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Spatial self-similarity is a hallmark of critical phenomena. We investigate the dynamic process of percolation, in which bonds are incrementally inserted to an empty lattice until fully occupied, and track the gaps describing the changes in cluster sizes. Surprisingly, we find that the gap sizes follow a universal power-law distribution throughout the whole or a significant portion of process, revealing a previously unrecognized temporal self-similarity. This phenomenon appears across various percolation models, like standard, explosive and rigidity percolation. Furthermore, in rigidity percolation, we directly observe a cascading cluster-merging dynamics, triggered by single bond insertion, and further obtain a distinct temporal self-similarity in the number of merged clusters, which are hidden in static analyses. Our results also suggest that, for rigidity percolation, the temporal self-similarity is probably more intrinsic than the spatial one. These findings offer a fresh perspective on critical phenomena and broaden potential applications across complex systems.