无标度网络上有限尺度的渗流

IF 5.6 1区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Xuewei Zhao , Liwenying Yang , Dan Peng , Run-Ran Liu , Ming Li
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引用次数: 0

摘要

度分布为pk ~ k−λ的无标度网络上的临界现象由于其结构非均质性而表现出丰富的有限尺寸效应。我们系统地研究了有限大小的渗透尺度,并确定了两种不同的平均场行为交叉路径:一种由度指数λ控制,另一种由度截止K ~ Vκ控制,其中V是系统大小,κ∈[0,1]是截止指数。增加λ或减少κ抑制异质性和驱动系统向平均场行为,在边际情况附近的对数修正。这些发现提供了从异质临界到同质临界交叉的统一图景。在交叉区,我们观察到丰富的有限大小现象,包括从消失到发散磁化率的转变,伪临界点的移位和波动的不同指数,以及先前理论预测的数值澄清。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Finite-size scaling of percolation on scale-free networks
Critical phenomena on scale-free networks with a degree distribution pkkλ exhibit rich finite-size effects due to its structural heterogeneity. We systematically study the finite-size scaling of percolation and identify two distinct crossover routes to mean-field behavior: one controlled by the degree exponent λ, the other by the degree cutoff KVκ, where V is the system size and κ[0,1] is the cutoff exponent. Increasing λ or decreasing κ suppresses heterogeneity and drives the system toward mean-field behavior, with logarithmic corrections near the marginal case. These findings provide a unified picture of the crossover from heterogeneous to homogeneous criticality. In the crossover regime, we observe rich finite-size phenomena, including the transition from vanishing to divergent susceptibility, distinct exponents for the shift and fluctuation of pseudocritical points, and a numerical clarification of previous theoretical predictions.
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来源期刊
Chaos Solitons & Fractals
Chaos Solitons & Fractals 物理-数学跨学科应用
CiteScore
13.20
自引率
10.30%
发文量
1087
审稿时长
9 months
期刊介绍: Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.
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