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Efficient Monte Carlo Algorithm and High-Precision Results for Percolation
Open accessAbstract
We present a new Monte Carlo algorithm for studying site or bond percolation on any lattice. The algorithm allows us to calculate quantities such as the cluster size distribution or spanning probability over the entire range of site or bond occupation probabilities from zero to one in a single run which takes an amount of time scaling linearly with the number of sites on the lattice. We use our algorithm to determine that the percolation transition occurs at p(c) = 0.592 746 21(13) for site percolation on the square lattice and to provide clear numerical confirmation of the conjectured 4/3-power stretched-exponential tails in the spanning probability functions.
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Cites
Introduction to Percolation Theory
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Epidemics and percolation in small-world networks
Moore, C., & Newman, M. E. J. (2000) · Physical Review E · doi:10.1103/physreve.61.5678 · Cited by 948
Self-citationSpanning probability in 2D percolation
Ziff, R. M. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2670 · Cited by 261
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Punctuated equilibrium and ‘‘history-dependent’’ percolation
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Unlocking the Potential of Cation-Disordered Oxides for Rechargeable Lithium Batteries
Lee, J., Urban, A., Li, X., Su, D., Hautier, G., & Ceder, G. (2014) · Science · doi:10.1126/science.1246432 · Cited by 1,248
Percolation on complex networks: Theory and application
Li, M., Liu, R.-R., Lü, L., Hu, M.-B., Xu, S., & Zhang, Y.-C. (2021) · Physics Reports · doi:10.1016/j.physrep.2020.12.003 · Cited by 365
Quantification of network structural dissimilarities
Schieber, T. A., Carpi, L., Díaz-Guilera, A., Pardalos, P. M., Masoller, C., & Ravetti, M. G. (2017) · Nature Communications · doi:10.1038/ncomms13928 · Cited by 237
Percolation in self-similar networks
Serrano, M. Á., Krioukov, D., & Boguñá, M. (2011) · Physical Review Letters · doi:10.1103/physrevlett.106.048701 · Cited by 47
Metadata
- Authors
- Newman, M. E. J., & Ziff, R. M.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2000-11-06
- Volume
- 85
- Issue
- 19
- Pages
- 4104-4107
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2072053277
- Cited by
- 503
- References
- 10
- FWCI
- 10.10
- Type
- journal article
- Language
- en
- Open access
- green
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