Open AccessNumerical simulations of the phase transition property of the explosive percolation model on Erds Rnyi random network
Author(s) -
Yan Li,
Tang Gang,
Song Li-Jiang,
Zhipeng Xun,
Hui Xia,
Dapeng Hao
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.046401
Subject(s) - percolation (cognitive psychology) , explosive material , statistical physics , scaling , directed percolation , phase transition , continuum percolation theory , percolation threshold , percolation critical exponents , percolation theory , cluster (spacecraft) , physics , critical exponent , topology (electrical circuits) , computer science , mathematics , condensed matter physics , quantum mechanics , combinatorics , electrical resistivity and conductivity , chemistry , geometry , organic chemistry , neuroscience , biology , programming language
Based on the modified Newman and Ziff algorithm combined with the finite-size scaling theory, in this present work we analytically study the phase transition property of the explosive percolation model induced by Achlioptas process on the Erds Rnyi 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 Erds Rnyi 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.