Tricritical Directed Percolation with Long-Range Spreading

Abstract

The effect of turbulent mixing on the model of tricritical directed percolation is studied. The turbulent advecting velocity field is modeled by means of the Kraichnan’s rapid change ensemble. The non-equilibrium critical phenomena of one-component reaction-diffusion systems are investigated employing field theoretic renormalization group technique. We give a brief overview of the field-theoretic approach to the problem including renormalization group analysis. The renormalization procedure is performed in the framework of double (ε, y)-expansion scheme, where the ε is the deviation from the upper critical dimension dc = 3 and the y is the exponent describing scaling behavior of velocity fluctuations. The corresponding asymptotic behavior is analyzed in leading order of perturbation theory.