网络模型中的局部化跃迁、Lifschitz尾和稀有区域效应
Localization transition, Lifschitz tails and rare-region effects in network models
摘要：
利用猝灭平均场论研究了疑似感染易感模型的异质性对网络的影响。本地化的出现所描述的分布的逆参与比和比较的稀有区域的影响出现在模拟和Lifschitz尾巴。后者，在线性近似下，与拉普拉斯矩阵的谱密度和依赖于时间的序参量有关。我表明，这些近似正确地表明格里菲斯阶段都定期一维晶格和小世界网络表现出纯粹的拓扑混乱。我讨论了发生在无标度网络上的$γ=3$度指数的局部化转变。
英文摘要：
Effects of heterogeneity in the suspected-infected-susceptible model on networks are investigated using quenched mean-field theory. The emergence of localization is described by the distributions of the inverse participation ratio and compared with the rare-region effects appearing in simulations and in the Lifschitz tails. The latter, in the linear approximation, is related to the spectral density of the Laplacian matrix and to the time dependent order parameter. I show that these approximations indicate correctly Griffiths Phases both on regular one-dimensional lattices and on small world networks exhibiting purely topological disorder. I discuss the localization transition that occurs on scale-free networks at $γ=3$ degree exponent.
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