Anomalous Dimensions of Leading Composite Operators in the Kinematic MHD Turbulence: Two-Loop Renormalization Group Analysis

Using the field theoretic renormalization group technique and the operator product expansion, the kinematic MHD turbulence is investigated in the second order (two-loop) approximation of the corresponding perturbative expansion. The anomalous dimensions of the leading composite operators, which drive the anomalous scaling of the single-time two-point correlation functions of the passive magnetic field, are calculated. It is shown that the two-loop corrections to these anomalous dimensions are significant and lead to the more anomalous (more negative) values of the total two-loop anomalous dimensions. It also means that the anomalous scaling at the two-loop level of approximation is much more pronounced in the present model of passive vector advection than in the analogous model of passive scalar quantity advected by the turbulent velocity field driven by the stochastic Navier–Stokes equation.