$K$ -选择性渗流：导致丰富相变库的简单模型
$K$-selective percolation: A simple model leading to a rich repertoire of phase transitions
摘要：
我们提出了$K$ -选择渗流过程作为复杂网络中具有特定中间度的节点的迭代移除模型。在该模型中，度为$K$的随机节点被逐个去激活，直到没有更多的度为$K$的节点剩余。在各种合成和现实世界的网络上的巨大的组件大小的非单调响应意味着一个结论，即网络可以通过删除更多的边缘，对这种选择性攻击更强大。在理论上，$K$ -选择性渗流过程表现出丰富的相变，包括混合和连续的双重相变，以及重入相变。值得注意的是，我们在Erdens-Rényi网络上观察到一个类似三临界点的点。我们还研究了简单立方晶格上的一个不连续跃迁，它具有不寻常的序参量涨落和分布，这在其他具有级联过程的渗流模型中是不存在的。最后，我们进行有限尺寸标度分析，以获得临界指数的各种过渡点，包括那些外来的。
英文摘要：
We propose the $K$-selective percolation process as a model for the iterative removals of nodes with the specific intermediate degree in complex networks. In the model, a random node with degree $K$ is deactivated one by one until no more nodes with degree $K$ remain. The non-monotonic response of the giant component size on various synthetic and real-world networks implies a conclusion that a network can be more robust against such selective attack by removing further edges. In the theoretical perspective, the $K$-selective percolation process exhibits a rich repertoire of phase transitions, including double transitions of hybrid and continuous, as well as reentrant transitions. Notably, we observe a tricritical-like point on Erdős-Rényi networks. We also examine a discontinuous transition with unusual order parameter fluctuation and distribution on simple cubic lattices, which does not appear in other percolation models with cascade processes. Finally, we perform finite-size scaling analysis to obtain critical exponents on various transition points, including those exotic ones.
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