Universal Scaling of Gap Dynamics in Percolation

TL;DR

This paper uncovers universal scaling laws in the dynamics of percolation, revealing self-similarity and Fisher exponents across various models and real systems, thus advancing the understanding of critical phenomena.

Contribution

It introduces a kinetic perspective and a novel scaling relation linking Fisher exponents, applicable to diverse percolation models and real-world systems, demonstrating universality in gap dynamics.

Findings

Identification of two independent Fisher exponents for critical and supercritical phases.

Proposal of a new scaling relation linking Fisher exponents with known critical exponents.

Demonstration of the theory's application to real systems for extracting Fisher exponents.

Abstract

Percolation is a cornerstone concept in physics, providing crucial insights into critical phenomena and phase transitions. In this study, we adopt a kinetic perspective to reveal the scaling behaviors of higher-order gaps in the largest cluster across various percolation models, spanning from latticebased to network systems, encompassing both continuous and discontinuous percolation. Our results uncover an inherent self-similarity in the dynamical process both for critical and supercritical phase, characterized by two independent Fisher exponents, respectively. Utilizing a scaling ansatz, we propose a novel scaling relation that links the discovered Fisher exponents with other known critical exponents. Additionally, we demonstrate the application of our theory to real systems, showing its practical utility in extracting the corresponding Fisher exponents. These findings enrich our understanding of percolation dynamics and highlight the robust and universal scaling laws that transcend individual models and extend to broader classes of complex systems.