Anomalous scaling of the magnetic field in the compressible Kazantsev-Kraichnan model: two-loop renormalization group analysis.

The field theoretic renormalization group and operator product expansion are used for an investigation of the anomalous scaling behavior of correlation functions of the weak magnetic field in the framework of the compressible Kazantsev-Kraichnan model. Two-loop expressions for the anomalous exponents of the correlation functions of arbitrary order in the presence of large-scale anisotropy are found as functions of compressibility. The influence of compressibility on the hierarchy of the anisotropic contributions is discussed, and it is shown that already relatively small compressibility can destroy the standard hierarchy of anisotropic anomalous exponents in the framework of which the leading contribution to the anomalous scaling is given by the isotropic shell.