Li Jiantong, Zhang Shi-Li
School of Information and Communication Technology, Royal Institute of Technology (KTH), Electrum 229, SE-164 40 Kista, Sweden.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):040104. doi: 10.1103/PhysRevE.80.040104. Epub 2009 Oct 19.
This work presents the generalization of the concept of universal finite-size scaling functions to continuum percolation. A high-efficiency algorithm for Monte Carlo simulations is developed to investigate, with extensive realizations, the finite-size scaling behavior of stick percolation in large-size systems. The percolation threshold of high precision is determined for isotropic widthless stick systems as Ncl2=5.637 26+/-0.000 02 , with Nc as the critical density and l as the stick length. Simulation results indicate that by introducing a nonuniversal metric factor A=0.106 910+/-0.000 009 , the spanning probability of stick percolation on square systems with free boundary conditions falls on the same universal scaling function as that for lattice percolation.
这项工作将通用有限尺寸标度函数的概念推广到连续渗流。开发了一种用于蒙特卡罗模拟的高效算法，通过大量的实现来研究大尺寸系统中棒状渗流的有限尺寸标度行为。对于各向同性无宽度棒状系统，确定了高精度的渗流阈值为Ncl2 = 5.637 26±0.000 02，其中Nc为临界密度，l为棒长。模拟结果表明，通过引入非通用度量因子A = 0.106 910±0.000 009，具有自由边界条件的方形系统上棒状渗流的跨越概率与晶格渗流的跨越概率落在相同的通用标度函数上。
