论文标题
$ n $ - 集体相关性的四维渗透率
$N$-cluster correlations in four- and five-dimensional percolation
论文作者
论文摘要
我们通过广泛的蒙特卡洛模拟研究了四维（4D，5D）键渗透的$ n $ clustruster相关功能。我们重新制定转移蒙特卡洛算法进行渗透[物理学。修订版E {\ bf 72}，016126（2005）]使用不连接集合数据结构，并模拟圆柱几何$ l^{d-1} \ times \ infty $，线性大小高达$ $ l = 512 $ for 4d且$ 128 $ 128 $ for 5d $。我们以高精度确定所有可能的$ n $ cluster指数，用于$ n \！ = \！2 $和$ 3 $，以及对数相关函数的通用幅度。从$ n \！ = \！2 $，我们将相关长度的关键指数作为$ 1/ν\！ = \！ 1.4610（12）$ 4D和$ 1/ν\！ = \！ 1.737（2）$ 5D，比现有结果显着改善。据我们所知，尚未对其他指数和通用对数幅度进行估计。我们的工作证明了对数综合场理论的有效性，并增加了不断增长的高维渗透知识。
We study $N$-cluster correlation functions in four- and five-dimensional (4D, 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E {\bf 72}, 016126 (2005)] using the disjoint-set data structure, and simulate a cylindrical geometry $L^{d-1}\times \infty$, with the linear size up to $L=512$ for 4D and $128$ for 5D. We determine with a high precision all possible $N$-cluster exponents, for $N \! =\!2$ and $3$, and the universal amplitude for a logarithmic correlation function. From the symmetric correlator with $N \! = \!2$, we obtain the correlation-length critical exponent as $1/ν\! =\! 1.4610(12)$ for 4D and $1/ν\! =\! 1.737 (2)$ for 5D, significantly improving over the existing results. Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge. Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.
