  The field theoretic renormalization group and the operator product expansion
are applied to the model of passive vector (magnetic) field advected by a
random turbulent velocity field. The latter is governed by the Navier--Stokes
equation for compressible fluid, subject to external random force with the
covariance $\propto \delta(t-t') k^{4-d-y}$, where $d$ is the dimension of
space and $y$ is an arbitrary exponent. From physics viewpoints, the model
describes magnetohydrodynamic turbulence in the so-called kinematic
approximation, where the effects of the magnetic field on the dynamics of the
fluid are neglected. The original stochastic problem is reformulated as a
multiplicatively renormalizable field theoretic model; the corresponding
renormalization group equations possess an infrared attractive fixed point. It
is shown that various correlation functions of the magnetic field and its
powers demonstrate anomalous scaling behavior in the inertial-convective range
already for small values of~$y$. The corresponding anomalous exponents,
identified with scaling (critical) dimensions of certain composite fields
("operators" in the quantum-field terminology), can be systematically
calculated as series in $y$. The practical calculation is performed in the
leading one-loop approximation, including exponents in anisotropic
contributions. It should be emphasized that, in contrast to Gaussian ensembles
with finite correlation time, the model and the perturbation theory presented
here are manifestly Galilean covariant.
