Geodesic
Critical behavior of percolation process influenced by a random velocity field: One–loop approximation
Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 79-88 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the perturbation renormalization group, we investigate the influence of a random velocity field on the critical behavior of the directed-bond percolation process near its second-order phase transition between the absorbing and active phases. We use the Antonov–Kraichnan model with a finite correlation time to describe the advecting velocity field. To obtain information about the large-scale asymptotic behavior of the model, we use the field theory renormalization group approach. We analyze the model near its critical dimension via a three-parameter expansion in $\epsilon$, $\delta$, and $\eta$, where $\epsilon$ is the deviation from the Kolmogorov scaling, $\delta$ is the deviation from the critical space dimension, and $\eta$ is the deviation from the parabolic dispersion law for the velocity correlator. We find the fixed points with the corresponding stability regions in the leading order in the perturbation scheme.
Keywords: perturbative renormalization group, directed percolation
Mots-clés : turbulent diffusion. 
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     title = {Critical behavior of percolation process influenced by a~random velocity field: {One{\textendash}loop} approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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M. Dančo; M. Gnatich; T. Lučivjanský; L. Mižišin. Critical behavior of percolation process influenced by a random velocity field: One–loop approximation. Teoretičeskaâ i matematičeskaâ fizika, Tome 176 (2013) no. 1, pp. 79-88. http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a7/

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