Wang Junfeng, Zhou Zongzheng, Zhang Wei, Garoni Timothy M, Deng Youjin
Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 May;87(5):052107. doi: 10.1103/PhysRevE.87.052107. Epub 2013 May 7.
We simulate the bond and site percolation models on a simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be p(c)(bond)=0.24881182(10) and p(c)(site)=0.3116077(2). By performing extensive simulations at these estimated critical points, we then estimate the critical exponents 1/ν=1.1410(15), β/ν=0.47705(15), the leading correction exponent y(i)=-1.2(2), and the shortest-path exponent d(min)=1.3756(3). Various universal amplitudes are also obtained, including wrapping probabilities, ratios associated with the cluster-size distribution, and the excess cluster number. We observe that the leading finite-size corrections in certain wrapping probabilities are governed by an exponent ≈-2, rather than y(i)≈-1.2.
我们在边长最大为(L = 512)的简单立方晶格上模拟键渗流模型和格点渗流模型，并估计渗流阈值为(p(c)(键)=0.24881182(10))以及(p(c)(格点)=0.3116077(2))。通过在这些估计的临界点进行广泛模拟，我们接着估计临界指数(1/ν = 1.1410(15))、(β/ν = 0.47705(15))、主导修正指数(y(i)= -1.2(2))以及最短路径指数(d(min)= 1.3756(3))。还获得了各种普适振幅，包括环绕概率、与簇大小分布相关的比率以及过剩簇数。我们观察到某些环绕概率中的主导有限尺寸修正由指数(≈ -2)支配，而非(y(i)≈ -1.2)。
