Choi Woosik, Chae Huiseung, Yook Soon-Hyung, Kim Yup
Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Aug;90(2):022123. doi: 10.1103/PhysRevE.90.022123. Epub 2014 Aug 20.
To understand the dependence of phase-transition natures in explosive percolations on space dimensions, the number n(cut) of cutting bonds (sites) and the fractal dimension d(CSC) of the critical spanning cluster (CSC) for the six different models introduced in Phys. Rev. E 86, 051126 (2012) are studied on two- and three-dimensional lattices. It is found that n(cut)(L→∞)=1 for the intrabond-enhanced models and the site models on the two-dimensional square lattice with lattice size L. In contrast, n(cut) for the intrabond-suppressed models scales as n(cut)≃L(d(cut)) with d(cut)=1. d(CSC)=2.00(1) is obtained for the intrabond-enhanced models and the site models, while d(CSC)=1.96(1)(<2) is obtained for the intrabond-suppressed models in two dimensions (2D). These results strongly support that the intrabond-enhanced models and the site models undergo the discontinuous transition in 2D, while the intrabond-suppressed models do the continuous transition in 2D. On the three-dimensional cubic lattice, we find that d(cut)>0 and d(CSC)=2.8(1)(<3) for all six models, which indicates that the models undergo the continuous transition. Based on the finite-size scaling analyses of mean cluster size and order parameter, all six models in 3D show nearly the same critical phenomena within numerical errors.
为了理解爆炸渗流中的相变性质对空间维度的依赖性，我们在二维和三维晶格上研究了《物理评论E》86, 051126 (2012)中引入的六种不同模型的切断键（位点）数量n(cut)和临界跨越簇（CSC）的分形维数d(CSC)。研究发现，对于晶格尺寸为L的二维方形晶格上的键内增强模型和位点模型，n(cut)(L→∞)=1。相比之下，键内抑制模型的n(cut)按n(cut)≃L(d(cut))缩放，其中d(cut)=1。对于键内增强模型和位点模型，d(CSC)=2.00(1)，而在二维（2D）中，键内抑制模型的d(CSC)=1.96(1)(<2)。这些结果有力地支持了键内增强模型和位点模型在二维中经历不连续转变，而键内抑制模型在二维中经历连续转变。在三维立方晶格上，我们发现所有六种模型的d(cut)>0且d(CSC)=2.8(1)(<3)，这表明这些模型经历连续转变。基于平均簇尺寸和序参量的有限尺寸缩放分析，三维中的所有六种模型在数值误差范围内显示出几乎相同的临界现象。
