Bond and Site Percolation in Three Dimensions

Abstract

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 $p_c(\mathrm{bond})=0.24881182(10)$ and $p_c(\mathrm{site})=0.3116077(2)$. By performing extensive simulations at these estimated critical points, we then estimate the critical exponents $1/\nu =1.1410(15)$, $\beta /\nu =0.47705(15)$, 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 $\approx -2$, rather than $y_i\approx -1.2$.

8 pages,6 figures

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