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

• DOI: 10.1007/s11232-013-0077-2
• Publication Date: 2013-08-07T09:18:42Z
• Authors: M. Dančo; M. Hnatich; T. Lučivjanský; L. Mižišin
• Keywords: Statistical Mechanics (cond-mat.stat-mech); 0103 physical sciences; FOS: Physical sciences; Chaotic Dynamics (nlin.CD); Nonlinear Sciences - Chaotic Dynamics; 01 natural sciences; Condensed Matter - Statistical Mechanics

Using perturbative renormalization group we investigate the influence of random velocity field on the critical behavior of directed bond percolation process near its second-order phase transition between absorbing and active phase. Antonov-Kraichnan model with finite correlation time is used for description of advecting velocity field. The field-theoretic renormalization group approach is applied for getting information about asymptotic large scale behavior of the model under consideration. The model is analyzed near its critical dimension through three-parameter expansion in ��, ��, ��, where �� is the deviation from the Kolmogorov scaling, �� is the deviation from the critical space dimension {d_c} and �� is the deviation from the parabolic dispersion law for the velocity correlator. Fixed points with corresponding regions of stability are determined to the leading order in the perturbation scheme.<br/>accepted for publication in Theoretical and Mathematical Physics<br/>