Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Inertial-range scaling behavior of high-order (up to order N=51) two-point correlation functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. Exponents of the powerlike asymptotic behavior of the correlation functions have been calculated in the one-loop approximation. These exponents are shown to depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to correlation functions have not been found.