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We consider combined rotational, magnetic, and thermal evolution of theneutron star during the accretion phase in a binary system. A rapidaccretion-driven decay of the magnetic field decreases substantially theefficiency of angular momentum transfer. As a result, the neutron star cannotspin up to periods shorter than some limiting value even if accretion is verylong and accretion rate is high. The proposed mechanism can explain adiscrepancy between the shortest detected period and minimal possible spinperiod of neutron stars.

The accretion rate and minimum spin period of accreting pulsars