Abstract
We study the mean-field approximation in the site-percolation problem. Using the analog of the Simon-Lieb inequality, we show that the mean-field critical probability is convergent to the exact value when the size of clusters tends to infinity. Applying this approximation to the one-dimensional further-neighbor percolation problem and calculating some critical coefficients, we prove that the asymptotic scaling relations predicted by the coherent-anomaly method are satisfied.
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Lipowski, A., Suzuki, M. Convergence of mean-field approximations in site percolation and application of CAM tod=1 further-neighbors percolation problem. J Stat Phys 69, 1–16 (1992). https://doi.org/10.1007/BF01053779
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DOI: https://doi.org/10.1007/BF01053779