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Convergence of mean-field approximations in site percolation and application of CAM to d=1 further-neighbors percolation problem
Authors:
- Adam Antoni Lipowski,
- Masuo Suzuki
Abstract
We study the mean-field approximation in the site-percolation problem. Using the analog of the Simon-Lieb inequality, we show that the mean-field critical probability is convergent to the exact value when the size of clusters tends to infinity. Applying this approximation to the one-dimensional further-neighbor percolation problem and calculating some critical coefficients, we prove that the asymptotic scaling relations predicted by the coherent-anomaly method are satisfied. © 1992 Plenum Publishing Corporation.
- Record ID
- UAM60c9b453a260432ca6943594b64b8dd7
- Author
- Journal series
- Journal of Statistical Physics, ISSN 0022-4715
- Issue year
- 1992
- Vol
- 69
- Pages
- 1-16
- ASJC Classification
- ;
- DOI
- DOI:10.1007/BF01053779 Opening in a new tab
- Language
- (en) English
- Score (nominal)
- 0
- Score source
- journalList
- Publication indicators
- = 1; = 1; : 1999 = 0.977; : 2006 (2 years) = 1.437 - 2007 (5 years) =1.685
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- Uniform Resource Identifier
- https://researchportal.amu.edu.pl/info/article/UAM60c9b453a260432ca6943594b64b8dd7/
- URN
urn:amu-prod:UAM60c9b453a260432ca6943594b64b8dd7
* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or PerishOpening in a new tab system.