TY - JOUR

T1 - Critical behaviour of the randomly stirred dynamical Potts model: Novel universality class and effects of compressibility

AU - Antonov, N. V.

AU - Kapustin, A. S.

PY - 2012

Y1 - 2012

N2 - Critical behaviour of a nearly critical system, subjected to vivid turbulent mixing, is studied by means of the field theoretic renormalization group. Namely, relaxational stochastic dynamics of a non-conserved order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The mixing is modelled by Kraichnan's rapid-change ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum $\propto k^{-d-\xi}$. It is shown that, depending on the symmetry group of the underlying Potts model, the degree of compressibility and the relation between the exponent $\xi$ and the space dimension $d$, the system exhibits various types of infrared (long-time, large-scale) scaling behaviour, associated with four different infrared attractors of the renormalization group equations. In addition to known asymptotic regimes (equilibrium dynamics of the Potts model and the passively advected scalar field), existence of a new, strongly non-equilibriu

AB - Critical behaviour of a nearly critical system, subjected to vivid turbulent mixing, is studied by means of the field theoretic renormalization group. Namely, relaxational stochastic dynamics of a non-conserved order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The mixing is modelled by Kraichnan's rapid-change ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum $\propto k^{-d-\xi}$. It is shown that, depending on the symmetry group of the underlying Potts model, the degree of compressibility and the relation between the exponent $\xi$ and the space dimension $d$, the system exhibits various types of infrared (long-time, large-scale) scaling behaviour, associated with four different infrared attractors of the renormalization group equations. In addition to known asymptotic regimes (equilibrium dynamics of the Potts model and the passively advected scalar field), existence of a new, strongly non-equilibriu

U2 - 10.1088/1751-8113/45/50/505001

DO - 10.1088/1751-8113/45/50/505001

M3 - Article

VL - 45

SP - 505001_1-20

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 50

ER -