This article is cited in 5 papers

Critical behavior of percolation process influenced by a random velocity field: One–loop approximation

M. Dančo^a, M. Gnatich^ab, T. Lučivjanský^ab, L. Mižišin<sup>b

a</sup> Institute of Experimental Physics of the Slovak Academy of Sciences, Košice, Slovakia
^b Faculty of Science, P. J. Šafárik University, Košice, Slovakia

Abstract: 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, turbulent diffusion.

Received: 19.12.2012

DOI: 10.4213/tmf8492

 English version: Theoretical and Mathematical Physics, 2013, 176:1, 898–905

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