  We consider combined rotational, magnetic, and thermal evolution of the
neutron star during the accretion phase in a binary system. A rapid
accretion-driven decay of the magnetic field decreases substantially the
efficiency of angular momentum transfer. As a result, the neutron star cannot
spin up to periods shorter than some limiting value even if accretion is very
long and accretion rate is high. The proposed mechanism can explain a
discrepancy between the shortest detected period and minimal possible spin
period of neutron stars.
