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Monte Carlo estimates of critical percolation probabilities

  • P. Dean (a1) and N. F. Bird (a1)

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In this paper we present results for the critical percolation probabilities of a number of two- and three-dimensional lattices. These results are based upon Monte Carlo studies of the way in which cluster-size distributions vary as the number of occupied sites in a lattice is progressively increased; the principle of the method has been described in some detail in an earlier publication (Dean (1)) in which the results of studies carried out on the ACE computer were reported. The use of a KDF 9 computer with a 32K word high-speed store has now enabled us to obtain results of a very high accuracy indeed; in those cases where our values for critical probabilities can be checked against exactly known values, they differ by no more than 0·1%.

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(1)Dean, P.Proc. Cambridge Philos. Soc. 59 (1963), 397.
(2)Frisch, H. L., Sonnenblick, E., Vyssotsky, V. A. and Hammersley, J. M.Phys. Rev. 124 (1961), 1021.
(3)Sykes, M. F. and Essam, J. W.Phys. Rev. 133 (1964), A 310.
(4)Sykes, M. F. and Essam, J. W.J. Math. Phys. 5 (1964), 1117.
(5)Vyssotsky, V. A., Gordon, S. B., Frisch, H. L. and Hammersley, J. M.Phys. Rev. 123 (1961), 1566.

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