Universality of explosive percolation under product and sum rule

作     者：Ziting Luo Wei Chen Jan Nagler 

作者机构：LMIB and School of Mathematical Sciences Beihang University Beijing 100191 China Institute of Artificial Intelligence Beihang University Beijing 100191 China Zhongguancun Laboratory Beijing 100094 People's Republic of China Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Beijing 100191 China Deep Dynamics Centre for Human and Machine Intelligence Frankfurt School of Finance and Management Frankfurt am Main 60322 Germany 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2023年第108卷第3期

页      面：034108-034108页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基　　金：Natural Science Foundation of Beijing Municipality  (Z180005) 

主　　题：Percolation phase transition 

摘      要：We study explosive percolation processes on random graphs for the so-called product rule (PR) and sum rule (SR), in which M candidate edges are randomly selected from all possible ones at each time step, and the edge with the smallest product or sum of the sizes of the two components that would be joined by the edge is added to the graph, while all other M−1 candidate edges are being discarded. These two rules are prototypical “explosive percolation rules, which exhibit an extremely abrupt yet continuous phase transition in the thermodynamic limit. Recently, it has been demonstrated that PR and SR belong to the same universality class for two competing edges, i.e., M=2. Here we investigate whether the claimed PR-SR universality is valid for higher-order models with M larger than 2. Based on traditional finite-size scaling theory and largest-gap scaling, we obtain the percolation threshold and the critical exponents of the order parameter, susceptibility, and the derivative of entropy for PR and SR for M from 2 to 9. Our results strongly suggest PR-SR universality, for any fixed M.