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Главная Публикации Probability of incipient spanning clusters in critical square bond percolation, L.N. Shchur and S.S. Kosyakov, 1997

Probability of incipient spanning clusters in critical square bond percolation

L.N. Shchur and S.S. Kosyakov

Int. J. Mod. Phys. C 8 (1997) 473-481



The probability of simultaneous occurence of at least k spanning clusters has been studied by Monte Carlo simulations on the 2D square lattice at the bond percolation threshold $p_c=1/2$. It is found that the probability of k and more Incipient Spanning Clusters (ISC) has the values $P(k>1) \approx 0.00658(3)$ and $P(k>2) \approx 0.00000148(21)$ provided that the limit of these probabilities for infinite lattices exists. The probability $P(k>3)$ of more than three ISC could be estimated to be of the order of 10^{-11} and is beyond the possibility to compute a such value by nowdays computers. So, it is impossible to check in simulations the Aizenman law for the probabilities when $k>>1$. We have detected a single sample with 4 ISC in a total number of about 10^{10} samples investigated. The probability of single event is 1/10 for that number of samples.

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