Anomalous scaling and large-scale anisotropy in magnetohydrodynamic turbulence: Two-loop renormalization-group analysis of the Kazantsev--Kraichnan kinematic model

TL;DR

This paper uses advanced renormalization-group techniques to analyze anomalous scaling and anisotropy in a magnetohydrodynamic turbulence model, providing detailed second-order calculations of correlation functions.

Contribution

It presents a two-loop renormalization-group analysis of the Kazantsev--Kraichnan model, including anisotropic effects and higher-order anomalous exponents.

Findings

Anomalous scaling is linked to operators with negative dimensions.

Second-order corrections strengthen anomalous scaling and anisotropic contributions.

Explicit calculations of correlation function exponents in the model.

Abstract

The field theoretic renormalization group and operator product expansion are applied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.