  We study the properties of solar magnetic fields on scales less than the
spatial resolution of solar telescopes. A synthetic infrared
spectropolarimetric diagnostics based on a 2D MHD simulation of
magnetoconvection is used for this. We analyze two time sequences of snapshots
that likely represent two regions of the network fields with their immediate
surrounding on the solar surface with the unsigned magnetic flux density of 300
and 140 G. In the first region we find from probability density functions of
the magnetic field strength that the most probable field strength at logtau_5=0
is equal to 250 G. Weak fields (B < 500 G) occupy about 70% of the surface,
while stronger fields (B 1000 G) occupy only 9.7% of the surface. The magnetic
flux is -28 G and its imbalance is -0.04. In the second region, these
parameters are correspondingly equal to 150 G, 93.3 %, 0.3 %, -40 G, and -0.10.
We estimate the distribution of line-of-sight velocities on the surface of log
tau_5=-1. The mean velocity is equal to 0.4 km/s in the first simulated region.
The averaged velocity in the granules is -1.2 km/s and in the intergranules is
2.5 km/s. In the second region, the corresponding values of the mean velocities
are equal to 0, -1.8, 1.5 km/s. In addition we analyze the asymmetry of
synthetic Stokes-V profiles of the Fe I 1564.8 nm line. The mean values of the
amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude
asymmetry is increased to 10% while the area asymmetry is only slightly varied.
