Critical Behavior of Percolation Process Influenced by Random Velocity Field: One-Loop Approximation

Abstract

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 ε, δ, η, where ε is the deviation from the Kolmogorov scaling, δ is the deviation from the critical space dimension {d_c} and η 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.

accepted for publication in Theoretical and Mathematical Physics

References in corpus (2)

• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models

Cited by in corpus (4)

• Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time
• Influence of turbulent mixing on critical behavior of directed percolation process : effect of compressibility
• Gribov process advected by the synthetic compressible velocity ensemble: Renormalization Group Approach
• Active-to-absorbing phase transition subjected to the velocity fluctuations in the frozen limit case