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Monte Carlo estimates of critical percolation probabilities

Published online by Cambridge University Press:  24 October 2008

P. Dean  and
N. F. Bird
P. Dean
Affiliation:
Mathematics Division, National Physical Laboratory, Teddington, Middlesex
N. F. Bird
Affiliation:
Mathematics Division, National Physical Laboratory, Teddington, Middlesex
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Extract

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%.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 477 - 479
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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