Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-25T02:14:51.253Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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