Unification of multiple classes of explosive percolation

¹ School of Physics and Electronic Engineering, Sichuan Normal University - Chengdu 610066, China
² School of Physics, University of Electronic Science and Technology of China - Chengdu 610054, China
³ School of Mathematical Sciences, University of Electronic Science and Technology of China Chengdu 611731, China

^(a) gaoyachun@uestc.edu.cn
^(b) zhangt512@foxmail.com

Received: 6 April 2019
Accepted: 22 August 2019

Abstract

Percolation, characterizing the emergence of large-scale connectivity from a great number of isolated nodes, can generate continuous, multiple discontinuous and discontinuous phase transitions, which correspond to different physical processes, respectively. In this paper, we found a percolation model which unifies all the three types of phase transitions with a continuously tunable parameter α. When decreasing α from 1 to 0, the type of phase transition transfers from continuous to multiple discontinuous, and finally the percolation process exhibits a single discontinuity lacking a supercritical region. By carefully examining the evolving characteristic of the clusters, it is verified that the transition value of α is between 0.75 and 0.7 for the phase transition from continuous to multiple discontinuous, and the distinctly different behaviors of the relative variance of the order parameter at and confirm the result. On the other hand, the transition value of α is 0.5 at which the type of phase transition changes from multiple discontinuous to discontinuous. These results may be helpful in understanding the physical mechanisms behind various percolation transition processes.