Effects of turbulent transfer on critical behavior

Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly nonequilibrium reaction–diffusion system, known as the Gribov process or directed percolation process. The turbulent mixing is modeled by the stochastic Navier–Stokes equation with a random stirring force with the correlator $\propto\delta(t-t')p^{4-d-y}$, where $p$ is the wave number, $d$ is the space dimension, and $y$ is an arbitrary exponent. We show that the systems exhibit various types of critical behavior depending on the relation between $y$ and $d$. In addition to known regimes (original systems without mixing and a passively advected scalar field), we establish the existence of new strongly nonequilibrium universality classes and calculate the corresponding critical dimensions to the first order of the double expansion in $y$ and $\varepsilon=4-d$ (one-loop approximation).