西尔潘斯基地毯上节点、边缘、引导和扩散渗流模型的相变

IF 2.8 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Hoseung Jang, Unjong Yu
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引用次数: 0

摘要

我们采用基于纽曼-齐夫算法的蒙特卡洛方法,在西尔潘斯基地毯上构建的三个分形图中研究了四种类型的渗滤模型--节点渗滤、边缘渗滤、引导渗滤和扩散渗滤。对于每种情况,我们都通过渗滤概率交叉和有限尺寸缩放分析,计算出渗滤阈值和临界指数(ν、γ 和 β),并结合了缩放修正效应。我们的结果表明,三种分形图中的渗滤相变临界指数在所有四种渗滤模型中都表现出普遍性。此外,我们还证明,如果用豪斯多夫维度代替空间维度 d,超尺度关系 dν=γ+2β 在西尔皮斯基地毯上的渗滤相变中也是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Phase transitions in the node, edge, bootstrap, and diffusion percolation models on the Sierpiński carpet
We investigate four types of percolation models — node, edge, bootstrap, and diffusion percolation — in three fractal graphs constructed on the Sierpiński carpet, employing the Monte Carlo method based on the Newman–Ziff algorithm. For each case, we calculate the percolation threshold and critical exponents (ν, γ, and β) through the crossing of percolation probabilities and the finite-size scaling analysis, incorporating correction-to-scaling effects. Our results reveal that critical exponents of the percolation phase transition in the three fractal graphs exhibit universality across all four percolation models. Furthermore, we demonstrate that the hyperscaling relation dν=γ+2β is also valid in the percolation phase transition on the Sierpiński carpet if the spatial dimension d is replaced by the Hausdorff dimension.
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来源期刊
CiteScore
7.20
自引率
9.10%
发文量
852
审稿时长
6.6 months
期刊介绍: Physica A: Statistical Mechanics and its Applications Recognized by the European Physical Society Physica A publishes research in the field of statistical mechanics and its applications. Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents. Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.
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