Percolation transitions in two dimensions
Percolation transitions in two dimensions
复制标题
DOI：
10.1103/physreve.78.031136
复制
发表时间：
2008-09-01
影响因子：
2.4
通讯作者：
Blote, Henk W. J.
中科院分区：
文献类型：
--
作者：
Feng, Xiaomei;Deng, Youjin;Blote, Henk W. J.
通过传递矩阵计算和蒙特卡罗模拟，研究了几种二维晶格上的键和位渗透模型。晶格包括具有最近邻键的正方形晶格、三角形晶格、蜂窝状晶格和切块晶格，以及具有最近邻键和次近邻键的正方形晶格。给出了孔雀石和格子的键渗阈值以及方形、蜂窝和格子的点渗阈值的计算结果。我们还包括了具有最近和次近邻键的方形晶格的键和位点渗透阈值。我们发现尺度的修正符合库仑气体理论和共形不变性理论预测的第二温度维X-t2=4。在一些情况下，有证据表明存在具有相同指数的附加项，但经过对数因子的修改。只有在三角晶格上的点渗问题中，这样的对数项才显得很小或不存在。发现与X-t2=4相关的幂律修正的振幅取决于相对于有限系统的圆柱形几何的晶格方向。
We investigate bond- and site-percolation models on several two-dimensional lattices numerically, by means of transfer-matrix calculations and Monte Carlo simulations. The lattices include the square, triangular, honeycomb kagome, and diced lattices with nearest-neighbor bonds, and the square lattice with nearest- and next-nearest-neighbor bonds. Results are presented for the bond- percolation thresholds of the kagome and diced lattices, and the site-percolation thresholds of the square, honeycomb, and diced lattices. We also include the bond- and site-percolation thresholds for the square lattice with nearest- and next-nearest-neighbor bonds. We find that corrections to scaling behave according to the second temperature dimension X-t2=4 predicted by the Coulomb gas theory and the theory of conformal invariance. In several cases there is evidence for an additional term with the same exponent, but modified by a logarithmic factor. Only for the site-percolation problem on the triangular lattice does such a logarithmic term appear to be small or absent. The amplitude of the power-law correction associated with X-t2=4 is found to be dependent on the orientation of the lattice with respect to the cylindrical geometry of the finite systems.