Mendelson K S
Physics Department, Marquette University, Milwaukee, Wisconsin 53233, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Dec;60(6 Pt A):6496-8. doi: 10.1103/physreve.60.6496.
Previous simulations of percolation on correlated square and cubic lattices [Phys. Rev. E 56, 6586 (1997)] have been extended to all of the common two-dimensional lattices, including triangular, square 1-2, honeycomb, and kagome. Simulations were performed on lattices of up to 1024x1024 sites. The results are independent of lattice size except, possibly, for a weak dependence at large correlation lengths. As in the previous studies, all results can be fit by a Gaussian function of the correlation length w, p(c)=p(infinity)(c)+(p(0)(c)-p(infinity)(c))e(-alpha w(2)). However, there is some evidence that this fit is not theoretically significant. For the self-matching triangular and the matching square and square 1-2 lattices, the percolation thresholds satisfy the Sykes-Essam relation p(c)(L)+p(c)(L*)=1.
先前对相关正方形和立方晶格上渗流的模拟[《物理评论E》56, 6586 (1997)]已扩展到所有常见的二维晶格，包括三角形、正方形1 - 2、蜂窝状和 Kagome晶格。模拟是在多达1024×1024个格点的晶格上进行的。结果与晶格大小无关，可能除了在大相关长度时有微弱依赖性。与先前的研究一样，所有结果都可以用相关长度w的高斯函数拟合，p(c)=p(∞)(c)+(p(0)(c)-p(∞)(c))e^(-αw²)。然而，有一些证据表明这种拟合在理论上并不显著。对于自匹配三角形以及匹配正方形和正方形1 - 2晶格，渗流阈值满足赛克斯 - 埃萨姆关系p(c)(L)+p(c)(L*) = 1。
