三维逾渗模型的同时拟合研究.docVIP

三维逾渗模型的同时拟合研究 徐枭1，王俊峰1,2，吕建平3，邓友金1 1 中国科学技术大学合肥微尺度物质科学国家实验室及近代物理系，合肥　 230026 2 合肥工业大学电子科学与应用物理学院，合肥　 230009 3 中国矿业大学物理系，徐州　 221116 摘要：我们模拟了一些三维格子上的键逾渗和点逾渗模型，包括钻石格，体心立方格，和面心 立方格。与简单立方格上 [Phys. Rev. E, 87 052107 (2013)] 所观察到的现象相似，相比于基于 集团尺寸分布的无量纲量，某些 wrapping 概率展示了更弱的有限尺度修正以及对偏离逾渗阈 值 pc 的敏感性，因而提供了一种确定 pc 的强有力的手段。我们同时拟合了各个模型的 wrapping 概率的数值数据，以便于普适参数在拟合中被前述模型所共享，从而显著地提高了 对 pc 的估计精度。 关键词：逾渗阈值，临界指数，同时拟合，有限尺寸标度 中图分类号： O414.2 Simultaneous analysis of three-dimensional percolation models XU Xiao1, WANG Jun-Feng1,2, LV Jian-Ping3, Deng You-Jin1 1 Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026 2 School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei 230009 3 Department of Physics, China University of Mining and Technology, Xuzhou 221116 Abstract: We simulate the bond and site percolation models on several three-dimensional lattices, including the diamond, body-centered cubic, and face-centered cubic lattices. As on the simple-cubic lattice [Phys. Rev. E, 87 052107 (2013)], it is observed that in comparison with dimensionless ratios based on cluster-size distribution, certain wrapping probabilities exhibit weaker ?nite-size corrections and are more sensitive to the deviation from percolation threshold pc, and thus provide a powerful means for determining pc. We analyze the numerical data of the wrapping probabilities simultaneously such that universal parameters are shared by the aforementioned models, and thus signi?cantly improved estimates of pc are obtained. Key words: percolation threshold, critical exponents, simultaneous ?ts, ?nite-size scaling 基 金 项 目： The Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20103402110053，NSFC under Grant No.and 作者简介： Xu Xiao（1988-），male，Master Degree Candidate. Correspondence author：Deng You-Jin （1974-），male， profess