  Astrophysical fluids are generically turbulent, which means that frozen-in
magnetic fields are, at least, weakly stochastic. Therefore realistic studies
of astrophysical magnetic reconnection should include the effects of stochastic
magnetic field. In the paper we discuss and test numerically the Lazarian &
Vishniac (1999) model of magnetic field reconnection of weakly stochastic
fields. The turbulence in the model is assumed to be subAlfvenic, with the
magnetic field only slightly perturbed. The model predicts that the degree of
magnetic field stochasticity controls the reconnection rate and that the
reconnection can be fast independently on the presence or absence of anomalous
plasma effects. For testing of the model we use 3D MHD simulations. To measure
the reconnection rate we employ both the inflow of magnetic flux and a more
sophisticated measure that we introduce in the paper. Both measures of
reconnection provide consistent results. Our testing successfully reproduces
the dependences predicted by the model, including the variations of the
reconnection speed with the variations of the injection scale of turbulence
driving as well as the intensity of driving. We conclude that, while anomalous
and Hall-MHD effects in particular circumstances may be important for the
initiation of reconnection, the generic astrophysical reconnection is fast due
to turbulence, irrespectively of the microphysical plasma effects involved.
This conclusion justifies numerical modeling of many astrophysical
environments, e.g. interstellar medium, for which plasma-effect-based
collisionless reconnection is not applicable.
