{
  "id": "1111.6238",
  "version": "v1",
  "published": "2011-11-27T08:58:35.000Z",
  "updated": "2011-11-27T08:58:35.000Z",
  "title": "Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model",
  "authors": [
    "N. V. Antonov",
    "A. V. Malyshev"
  ],
  "comment": "21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial text overlap with arXiv:cond-mat/0607019",
  "journal": "J. Phys. A: Math. Theor. 45 (2012) 255004",
  "doi": "10.1088/1751-8113/45/25/255004",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-11-27T08:58:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76F30"
    ],
    "keywords": [
      "renormalization group analysis",
      "critical behaviour",
      "potts model",
      "turbulent mixing",
      "strongly anisotropic"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2012,
      "month": "Jun",
      "volume": 45,
      "number": 25,
      "pages": 255004
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JPhA...45y5004A"
    }
  }
}