多层网络上的逾渗相变

 逾渗模型的机制虽然简单，但是它涉及到统计物理与非线性物理中的众多理论与问题，在一些网络化的自然、技术与社会系统中，逾渗模型都得到成功应用。近年来，为了刻画更为复杂的相互作用系统，多层网络的概念被提出。而相应系统上的逾渗问题研究，也进一步引起研究人员关注。在这些研究中，逾渗模型不但成功解决了一些现实问题，其本身也展现出一些新现象，例如不连续相变。本文介绍了多层网络上逾渗模型的基本机制及相关连通性的度量，讨论了其中不连续相变的涌现与系统维度的关系，并对相关理论解析方法做简单介绍。

Percolation transition on multilayer networks

The percolation model describes the emergence of a giant component in a system, of which the sites are connected randomly with some mechanisms. Although the rule is very simple, the percolation model involves many concepts of statistical physics and nonlinear physics, and has also been applied to a large variety of natural, technological and social systems, most of which can be viewed as networks. In recent years, a new kind of networks, the multilayer networks, have been proposed to study the complex and interacting systems. Based on the percolation in these networks, a number of natural, technological and social problems have been solved. At the same time, the percolation transition itself also has some new properties, such as the discontinuous transition. This paper analyzes the mechanism of the percolation on multilayer networks first, and then briefly discusses the discontinuous transition in this model. Furthermore, the theoretical methods are also be reviewed.