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The field theoretic renormalization group and operator product expansion areapplied to the Kazantsev--Kraichnan kinematic model for the magnetohydrodynamicturbulence. The anomalous scaling emerges as a consequence of the existence ofcertain composite fields ("operators") with negative dimensions. The anomalousexponents for the correlation functions of arbitrary order are calculated inthe two-loop approximation (second order of the renormalization-groupexpansion), including the anisotropic sectors. The anomalous scaling and thehierarchy of anisotropic contributions become stronger due to thosesecond-order contributions.

physical review. e, statistical, nonlinear and soft matter physics

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