爆发性逾渗模型的Shortest-path指数和Backbone指数

Shortest-path Exponent and Backbone Exponent of Explosive Percolation Model

Shortest-path指数dmin和Backbone指数dB是统计物理中刻画相变普适类的两个重要的临界指数,由于缺少精确解,人们只能通过数值方法,尤其是蒙特卡洛模拟对其进行数值估计。本文通过在完全构型上取样图形距离和在bridge-free构型上取样最大集团大小,首次估计了正方晶格上遵守乘积规则的爆发性逾渗模型的Shortest-path指数和Backbone指数,分别为dmin=1.189(3)和dB=1.546(5)。本文的结果为人们后续解析地研究具有非平凡规则的逾渗模型的临界几何性质提供了重要的检验基础。

The Shortest-path exponent dmin and the Backbone exponent dB 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 dmin and dB 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 dmin=1.189(3) and dB=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.