Tuesday, February 5, 2013

1302.0421 (Junfeng Wang et al.)

Bond and Site Percolation in Three Dimensions    [PDF]

Junfeng Wang, Zongzheng Zhou, Wei Zhang, Timothy M. Garoni, Youjin Deng
We simulate the bond and site percolation models on the simple-cubic lattice with linear sizes up to L=512, and estimate the percolation thresholds to be $p_c ({\rm bond})=0.248\,811\,82(10)$ and $p_c ({\rm site})=0.311\,607\,7(2)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1/\nu =1.141\,0(15)$, $\beta/\nu=0.477\,05(15)$, the leading correction exponent $y_i =-1.2(2)$, and the shortest-path exponent $\dm=1.375\,6(3)$. 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 $\approx -2$, rather than $y_i \approx -1.2$.
View original: http://arxiv.org/abs/1302.0421

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