Critical behaviour of the randomly stirred dynamical Potts model: novel universality class and effects of compressibility

Abstract

Critical behaviour of the dynamical Potts model, subjected to vivid turbulent mixing, is studied by means of the renormalization group. The advecting velocity field is modelled by Kraichnan’s rapid-change ensemble: Gaussian statistics with a given pair correlator 〈vv〉∝δ(t − t′) k−d − ξ, where k is the wave number, d is the dimension of space and 0 < ξ < 2 is an arbitrary exponent. The system exhibits different types of infrared scaling behaviour, associated with four infrared attractors of the renormalization group equations. In addition to the known asymptotic regimes (equilibrium Potts model and passive scalar field), the existence of a new, strongly non-equilibrium type of critical behaviour (universality class) is established, where the self-interaction of the order parameter and the turbulent mixing are equally important. The corresponding critical dimensions and the regions of stability for all the regimes are calculated in the leading order of the double expansion in ξ and ε = 6 − d. Special attention is paid to the effects of compressibility of the fluid, because they lead to interesting crossover phenomena.