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.

percolation  /  multilayer networks  /  phase transition