CAJ | 학술논문

基于改进的Newman和Ziff算法以及有限尺寸标度理论,通过对表征渗流相变特征物理量的序参量、平均集团尺寸、二阶矩、标准偏差及尺寸不均匀性的数值模拟,分析研究了Erd¨os R′enyi随机网络上Achlioptas爆炸渗流模型的相变性质.研究表明:尽管序参量表现出了不连续相变的特征,但序参量以及其他特征物理量仍具有连续相变的幂律标度行为.因此严格地说, Erd¨os R′enyi随机网络中的爆炸渗流相变是一种奇异相变,它既不是标准的不连续相变,又与常规随机渗流表现出的连续相变处于不同的普适类.
기우개진적Newman화Ziff산법이급유한척촌표도이론,통과대표정삼류상변특정물리량적서삼량、평균집단척촌、이계구、표준편차급척촌불균균성적수치모의,분석연구료Erd¨os R′enyi수궤망락상Achlioptas폭작삼류모형적상변성질.연구표명:진관서삼량표현출료불련속상변적특정,단서삼량이급기타특정물리량잉구유련속상변적멱률표도행위.인차엄격지설, Erd¨os R′enyi수궤망락중적폭작삼류상변시일충기이상변,타기불시표준적불련속상변,우여상규수궤삼류표현출적련속상변처우불동적보괄류.
Based on the modified Newman and Ziff algorithm combined with the finite-size scaling theory, in this present work we ana-lytically study the phase transition property of the explosive percolation model induced by Achlioptas process on the Erd¨os R′enyi random network via numerical simulations for the basic percolation quantities including the order parameter, the average cluster size, the moments, the standard deviation and the cluster heterogeneity. It is explicitly shown that all these relevant quantities display a typical power-law scaling behavior, which is the characteristic of continuous phase transition at the percolation threshold despite the fact that the order parameter presents a certain feature of discontinuous transition at the same time. Strictly, the explosive percolation transition during the Erd¨os R′enyi random network is a singular transition, which means that it is neither a standard discontinuous phase transition nor the continuous transition in the regular random percolation model.