Yang Liwenying, Li Ming
School of Physics, <a href="https://ror.org/02czkny70">Hefei University of Technology</a>, Hefei, Anhui 230009, China.
Phys Rev E. 2024 Jul;110(1-1):014122. doi: 10.1103/PhysRevE.110.014122.
By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intracluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters. However, the volume fractal dimension d_{f}^{'} of biconnected clusters varies depending on the competition rules of intracluster bonds. The size distribution of biconnected clusters exhibits double-scaling behavior: large clusters follow the standard Fisher exponent derived from the hyperscaling relation τ^{'}=1+1/d_{f}^{'}, while small clusters display a modified Fisher exponent τ_{0}<τ^{'}. These findings provide insights into the intricate nature of connectivity in explosive percolation.
通过在随机图中引入一种简单的键插入竞争机制，爆发性渗流呈现出具有丰富临界现象的尖锐相变。我们使用基于事件的系综研究爆发性渗流中的高阶连通性，重点关注双连通簇，其中任意两个位点通过至少两条独立路径相连。我们的数值分析证实，具有不同簇内键竞争规则的爆发性渗流具有相同的渗流阈值和普适性，双连通簇与单连通簇同时发生渗流。然而，双连通簇的体积分形维数(d_{f}^{'})取决于簇内键的竞争规则。双连通簇的尺寸分布呈现双标度行为：大簇遵循从超标度关系(\tau^{'}=1+1/d_{f}^{'})导出的标准费希尔指数，而小簇显示出修正的费希尔指数(\tau_{0}<\tau^{'})。这些发现为爆发性渗流中连通性的复杂本质提供了见解。
