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A new Monte Carlo method for percolation problems on a lattice

Published online by Cambridge University Press:  24 October 2008

P. Dean
P. Dean
Affiliation:
Mathematics Division, National Physical Laboratory, Teddington
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Abstract

A new and general Monte Carlo technique is described for solving some well-known percolation and cluster-size problems on regular lattice networks. The method has been applied to ten two-dimensional structures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 2 , April 1963 , pp. 397 - 410
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Broadbent, S. R., and Hammersley, J. M., Proc. Cambridge Philos. Soc. 53 (1957), 629.Google Scholar
(2)Domb, C., and Sykes, M. F., Phys. Rev. 122 (1961), 77.CrossRefGoogle Scholar
(3)Elliot, R. J., Heap, B. R., Morgan, D. J., and Rushbrooke, G. S., Phys Rev. Letters, 5 (1960), 366.CrossRefGoogle Scholar
(4)Fisher, M. E., J. Mathematical Phys. 4 (1961), 620.CrossRefGoogle Scholar
(5)Fisher, M. E., and Essam, J. W., J. Mathematical Phys. 4 (1961), 609.CrossRefGoogle Scholar
(6)Frisch, H. L., Sonnenblick, E., Vyssotsky, V. A., and Hammersley, J. M., Phys. Rev. 124 (1961), 1021.CrossRefGoogle Scholar
(7)Hammersley, J. M., J. Mathematical Phys. 2 (1961), 728.Google Scholar
(8)Rushbrooke, G. S., and Morgan, D. J., J. Molecular Phys. 4 (1961), 1.Google Scholar
(9)Sato, M., Arrott, A., and Kikuchi, R., J. Phys. Chem. Solids, 10 (1959), 19.Google Scholar
(10)Vyssotsky, V. A., Gordon, S. B., Frisch, H. L., and Hammersley, J. M., Phys. Rev. 123 (1961), 1566.Google Scholar