Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2011-11-27
Physics
Condensed Matter
Statistical Mechanics
21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial text overlap with arXiv:cond-mat/0607019
Scientific paper
Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with correlation function of the form $\propto \delta(t-t') /|{\bf k}_{\bot}|^{d-1+\xi}$, where ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow") --- the $d$-dimensional generalization of the ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.} {\bf 131} 381] within the context of passive scalar advection. This model can describe a rich class of physical situations. It is shown that, depending on the values of parameters that define self-interaction of the order parameter and the relation between the exponent $\xi$ and the space dimension $d$, the system exhibits various types of large-scale scaling behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. In addition to known asymptotic regimes (critical dynamics of the Potts model and passively advected field without self-interaction), existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the leading order of the double expansion in $\xi$ and $\epsilon=6-d$ (one-loop approximation). The scaling appears strongly anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.
Antonov Nikolaj V.
Malyshev Victor A.
No associations
LandOfFree
Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-687071