Extensive population synthesis of isolated neutron stars with field decay

We perform population synthesis studies of different types of neutron stars taking into account the magnetic field decay. For the first time, we confront our results with observations using {it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $dot P$ diagram. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $<log (B_0/[G]) > sim 13.25$ and $sigma_{log B_0}sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible. We apply the obtained field distribution and the model of decay to study long-term evolution of neuton stars till the stage of accretion from the interstellar medium. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars ($B_0 > sim 10^{13}$ G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.