Profile and scaling of the fractal exponent of percolations in complex networks
Profile and scaling of the fractal exponent of percolations in complex networks
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DOI：
10.1209/0295-5075/104/16006
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
T. Hasegawa;T. Nogawa;Koji Nemoto
中科院分区：
文献类型：
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作者：
T. Hasegawa;T. Nogawa;Koji Nemoto
我们提出了一种新的有限尺度分析在复杂网络中观察到的逾渗过渡。在成长型网络中，合作系统通常会经历一个具有反Berezinskiii-Kosterlitz-无奇异性的无穷阶跃迁，数值模拟很难精确确定跃迁点.由于有序相的近邻不是简单的无序相，而是临界相，传统的有限尺寸标度技术不起作用。在我们的有限尺寸标度中，序参数和分形指数的标度函数的形式在数值上确定了无限阶过渡以及标准二阶过渡的过渡点和临界指数。我们确认我们的标度假设的有效性，通过Monte Carlo模拟键在一些网络模型：装饰（2，2）-花和随机附件增长网络，其中发生无限阶过渡，和配置模型，其中发生二阶过渡。
We propose a novel finite-size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite-order transition with inverted Berezinskii-Kosterlitz-Thouless singularity, it is very hard for numerical simulations to determine the transition point precisely. Since the neighbor of the ordered phase is not a simple disordered phase but a critical phase, conventional finite-size scaling technique does not work. In our finite-size scaling, the forms of the scaling functions for the order parameter and the fractal exponent determine the transition point and critical exponents numerically for an infinite-order transition as well as a standard second-order transition. We confirm the validity of our scaling hypothesis through Monte Carlo simulations for bond percolations in some network models: the decorated (2,2)-flower and the random attachment growing network, where an infinite-order transition occurs, and the configuration model, where a second-order transition occurs.