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Critical Percolation Probabilities by Series Methods
Abstract
Series estimates of the critical percolation probabilities for the "bond problem" and the "site problem" are presented for two- and three-dimensional lattices. Good agreement with the Monte Carlo estimates of Frisch et al. and of Dean is obtained. The series method gives information on the critical behavior of the mean cluster size and it is found that there is a much sharper growth of large clusters in two dimensions than in three dimensions as the critical concentration is approached from below.
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Citations
Cited by
Hopping Conductivity in Disordered Systems
Ambegaokar, V., Halperin, B. I., & Langer, J. S. (1971) · Physical Review B · doi:10.1103/physrevb.4.2612 · Cited by 1,917
Percolation and conductivity: A computer study. I
Pike, G. E., & Seager, C. H. (1974) · Physical Review B · doi:10.1103/physrevb.10.1421 · Cited by 1,031
Essam, J. W. (1980) · Reports on Progress in Physics · doi:10.1088/0034-4885/43/7/001 · Cited by 1,018
Self-citationPercolation Theory and Electrical Conductivity
Last, B. J., & Thouless, D. J. (1971) · Physical Review Letters · doi:10.1103/physrevlett.27.1719 · Cited by 503
Metadata
- Authors
- Sykes, M. F., & Essam, J. W.
- Venue
- Physical Review
- Publisher
- American Physical Society (APS)
- Published
- 1964-01-06
- Volume
- 133
- Issue
- 1A
- Pages
- A310-A315
- ISSN
- 0031-899X (ISSN-L)
- OpenAlex
- W2060143734
- Cited by
- 319
- References
- 0
- FWCI
- 2.23
- Type
- journal article
- Language
- en
- Open access
- closed
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- Sykes, M. F., & Essam, J. W. (1964). Critical Percolation Probabilities by Series Methods. Physical Review. https://doi.org/10.1103/physrev.133.a310
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