规则随机网络和Erdens-Rényi网络上扩散和自举逾渗模型的相变
Phase transition in the diffusion and bootstrap percolation models on regular random and Erdős-Rényi networks
摘要：
利用改进的Newman-Ziff算法研究了规则随机网络和Erdens-Rényi网络中的扩散渗流模型和自举渗流模型.计算了逾渗阈值和逾渗转变的序参量（巨团簇强度）及其导数。根据实验结果对渗流相变进行了分类。小$k$的扩散逾渗具有双重相变，而$m\geq3$的自举逾渗具有一级逾渗相变。$k$较大时的扩散渗流和$m$较小时的自举渗流均表现为二级渗流相变。特别地，在规则的随机网络中，在$m=2$的自举渗流中发现了三级渗流转变。
英文摘要：
The diffusion and bootstrap percolation models were studied in regular random and Erdős-Rényi networks using the modified Newman-Ziff algorithms. We calculated the percolation threshold and the order parameter of the percolation transition (strength of the giant cluster) and its derivatives. The percolation transitions are classified by the results. The diffusion percolation with a small $k$ has a double transition, and the bootstrap percolation with $m\geq3$ has the first-order percolation transition. The diffusion percolation with a large $k$ and the bootstrap percolation with a small $m$ show the second-order percolation transition. Particularly, third-order percolation transitions were discovered in the bootstrap percolation of $m=2$ in regular random networks.
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