Oriented Percolation in One–dimensional 1/|x−y|2 Percolation Models

Oriented Percolation in One–dimensional 1/|x−y|2 Percolation Models

We consider independent edge percolation models on ℤ, with edge occupation probabilities We prove that oriented percolation occurs when β >1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104:547, 1986 ). The proof is based on...

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Veröffentlicht in:Journal of statistical physics 2010-06, Vol.139 (6), p.941-959
Hauptverfasser: Marchetti, D. H. U., Sidoravicius, V., Vares, M. E.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Theoretical
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Zusammenfassung:We consider independent edge percolation models on ℤ, with edge occupation probabilities We prove that oriented percolation occurs when β >1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104:547, 1986 ). The proof is based on multi-scale analysis.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-010-9966-z