爆发性逾渗模型的Shortest-path指数和Backbone指数

doi:10.16088/j.issn.1001-6600.2020.02.009

Abstract

Abstract: The Shortest-path exponent d_min and the Backbone exponent d_B are two important critical exponents for characterizing the universality class in phase transition in statistical physics. Due to the lack of exact solutions, the values of d_min and d_B can only be estimated by numerical methods, such as Monte Carlo simulation (MC). In this paper, by sampling the graph distance on the complete configuration and the size of the largest cluster on the bridge-free configuration, for the first time, the shortest-path and backbone exponents are estimated for the square-lattice explosive percolation with product rule as d_min=1.189(3) and d_B=1.546(5), respectively. The results provide important testing foundations for the future analytical investigations of the critical geometrical properties of the percolation models with non-trivial rules.

Key words: percolation, critical exponent, Monte Carlo simulation, finite-size scaling

CLC Number:

O414.21

WANG Junfeng, LI Ping. Shortest-path Exponent and Backbone Exponentof Explosive Percolation Model[J].Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(2): 81-86.

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Shortest-path Exponent and Backbone Exponentof Explosive Percolation Model

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