Anomalous scaling in the Kazantsev-Kraichnan model with finite time correlations: two-loop renormalization group analysis of relevant composite operators

Eva Jurčišinová, Marian Jurčišin () and Martin Menkyna
Additional contact information
Eva Jurčišinová: Institute of Experimental Physics, Slovak Academy of Sciences
Marian Jurčišin: Institute of Experimental Physics, Slovak Academy of Sciences
Martin Menkyna: Institute of Experimental Physics, Slovak Academy of Sciences

The European Physical Journal B: Condensed Matter and Complex Systems, 2018, vol. 91, issue 12, 1-23

Abstract: Abstract The field theoretic renormalization group technique together with the operator product expansion in the second order of the perturbation theory (in the two-loop approximation) is used for the investigation of the influence of the finite time correlations of the velocity field on the anomalous dimensions of the leading set of composite operators, which drive the anomalous scaling of correlation functions of a weak magnetic field in the framework of the kinematic Kazantsev–Kraichnan model in the presence of a large scale anisotropy. The system of possible scaling regimes of the model is found and two important special limits of the model are briefly discussed. The general two-loop expressions for the anomalous and critical dimensions of the leading composite operators are found as functions of the spatial dimension d and of the renormalization group fixed point value of the parameter u, which drives the presence of the finite time correlations of the velocity field in the model. The anisotropic hierarchies among various anomalous dimensions are investigated and it is shown that, regardless of the fixed point value of the parameter u as well as regardless of the spatial dimension of the system, the leading role in the anomalous scaling properties of the model is played by the anomalous dimensions of the composite operators near the isotropic shell, in accordance with the Kolmogorov’s local isotropy restoration hypothesis. The properties of the anomalous dimensions of the leading composite operators in the Kazantsev–Kraichnan model with finite time correlations of the velocity field are compared to the properties of the corresponding anomalous dimensions of the composite operators relevant in the framework of the Kraichnan model of passively advected scalar field with finite time correlations. It is shown that, regardless of the fixed point value of the parameter u, the two-loop corrections to the anomalous dimensions are much more important in the framework of the Kazantsev–Kraichnan vector model than in the Kraichnan model of a passive scalar advection. At the same time, again regardless of the strength of time correlations, the two-loop values of the leading anomalous dimensions in the Kazantsev–Kraichnan model of the passive magnetic field are significantly more negative than the corresponding two-loop values of the relevant anomalous dimensions in the framework of the Kraichnan model. It means that the anomalous scaling of the correlation functions of the passive magnetic field, deep inside the inertial interval of the turbulent environment with finite time correlations of the velocity field, must be much more pronounced than in the case of the correlation functions of the passively advected scalar field. Graphical abstract

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/e2018-90511-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:91:y:2018:i:12:d:10.1140_epjb_e2018-90511-0

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/e2018-90511-0

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().