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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TMF_2013_176_1_a7,
     author = {M. Dan\v{c}o and M. Gnatich and T. Lu\v{c}ivjansk\'y and L. Mi\v{z}i\v{s}in},
     title = {Critical behavior of percolation process influenced by a~random velocity field: {One--loop} approximation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {79--88},
     publisher = {mathdoc},
     volume = {176},
     number = {1},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a7/}
}
TY  - JOUR
AU  - M. Dančo
AU  - M. Gnatich
AU  - T. Lučivjanský
AU  - L. Mižišin
TI  - Critical behavior of percolation process influenced by a~random velocity field: One--loop approximation
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2013
SP  - 79
EP  - 88
VL  - 176
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a7/
LA  - ru
ID  - TMF_2013_176_1_a7
ER  - 
%0 Journal Article
%A M. Dančo
%A M. Gnatich
%A T. Lučivjanský
%A L. Mižišin
%T Critical behavior of percolation process influenced by a~random velocity field: One--loop approximation
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2013
%P 79-88
%V 176
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2013_176_1_a7/
%G ru
%F TMF_2013_176_1_a7
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/