摘 要：随机演化网络中的BFW渗流模型具有的强不连续相变以及多重巨型分支稳定共存的特性引起了统计物理学家的广泛关注。本文基于混合连边机制，提出了修改的BFW模型。大量模拟实验表明存在一个调控参数的临界点。当偏好连边概率大于该临界点时，生成网络的度分布呈现幂律分布；而小于临界点时，生成网络的度分布呈现泊松分布。进一步对该模型渗流特性的分析结果表明，当偏好概率大于临界点时，模型具有多级相变；而小于临界点时，只有一次相变发生。更有趣的是，当偏好概率小于临界点时，序参量在热力学极限下是自平均的。相反，序参量会出现随机震荡现象，且在热力学极限下不具有自平均性质。
关键词：随机网络；渗流；多级相变；自平均
作者介绍：
王睿婕（1989-），女，汉，四川新津人，研究实习员，硕士研究生。研究方向：复杂网络。
中图分类号：N94；O357.3 文献标识码：A 文章编号：2096-4706（2018）02-0000-03
Network evolution and percolation phase transition based on mixed link mechanism
WANG Ruijie
（ABA Teachers University，Aba 623002，China）
Abstract：The characteristicsof the discontinuous percolation at the transition point and multiple giantcomponents coexist in the supercritical region of the BFW model on randomnetwork has attracted much attention from physicists and statisticians. Amodified BFW percolation model is proposed by changing the way of selecting thecandidate edge. Through large numbers of numerical simulations，we find thatthere exists a critical point，which separates the typeof the network structure. If the probability of the preferential attachment excessesthe critical point，the network degree exhibits apower-law distribution. Otherwise，the network degree ispoisson distribution. Additionally，the percolation processof the modified BFW model is researched. Simulation results indicate that thepercolation undergoes multi-transition when the probability of the preferentialattachment excesses the critical point. More interestingly，order parameter has random fluctuations when the probability of the preferentialattachment excesses the critical point.
Keywords：random network；percolation；multiple-transition；self-averaging
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