Effects of mixing and stirring on the critical behavior

TL;DR

This paper investigates how mixing and stirring influence the critical behavior of a scalar order parameter near phase transition points, revealing multiple scaling regimes and identifying new universality classes through advanced renormalization group analysis.

Contribution

It introduces a comprehensive field theoretic model incorporating stochastic stirring and mixing, uncovering three novel nonequilibrium universality classes with calculated critical dimensions.

Findings

Identification of several scaling regimes depending on parameters

Discovery of three new nonequilibrium universality classes

Calculation of critical dimensions in two-loop approximation

Abstract

Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random external Gaussian noise with the correlation function $\propto\delta(t-t') k^{4-d-y}$ and the divergence-free (due to incompressibility) velocity field, governed by the stochastic Navier--Stokes equation with a random Gaussian force with the correlation function $\propto\delta(t-t') k^{4-d-y'}$. Depending on the relations between the exponents $y$ and $y'$ and the space dimensionality $d$, the model reveals several types of scaling regimes. Some of them are well known (model A of equilibrium critical dynamics and linear passive scalar field advected by a random turbulent flow), but there are three new nonequilibrium regimes (universality classes) associated with new nontrivial fixed points of the renormalization group equations. The corresponding critical dimensions are calculated in the two-loop approximation (second order of the triple expansion in $y$, $y'$ and $\epsilon=4-d$).