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摘要翻译：
我们考虑了二维临界逾渗团簇的密度，这些临界逾渗团簇在无限条带、半无限条带和正方形中被限制在一个或两个边界上，以及无限条带中的几个相关量。我们的理论结果遵循共形场理论，并与高精度数值模拟进行了比较。例如，我们证明了在单位宽度的无限长条带（即交叉团簇）的两个边界上，团簇的密度与$(\sin\piy)^{-5/48}\{[\cos(\piy/2)]^{1/3}+[\sin(\piy/2)]^{1/3}-1\}$成正比。我们还从数值上确定了穿过正方形和边开边界的长矩形的团簇密度的等值线，并与理论上的沿边密度进行了比较。
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英文标题：
《The density of critical percolation clusters touching the boundaries of
strips and squares》
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作者：
Jacob J. H. Simmons, Peter Kleban, Kevin Dahlberg, Robert M. Ziff
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Disordered Systems and Neural Networks 无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
We consider the density of two-dimensional critical percolation clusters, constrained to touch one or both boundaries, in infinite strips, half-infinite strips, and squares, as well as several related quantities for the infinite strip. Our theoretical results follow from conformal field theory, and are compared with high-precision numerical simulation. For example, we show that the density of clusters touching both boundaries of an infinite strip of unit width (i.e. crossing clusters) is proportional to $(\sin \pi y)^{-5/48}\{[\cos(\pi y/2)]^{1/3} +[\sin (\pi y/2)]^{1/3}-1\}$. We also determine numerically contours for the density of clusters crossing squares and long rectangles with open boundaries on the sides, and compare with theory for the density along an edge.
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PDF链接：
https://arxiv.org/pdf/704.0901
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