  We study the current sample of rapidly rotating neutron stars in both
accreting and non-accreting binaries in order to determine whether the spin
distribution of accreting neutron stars in low-mass X-ray binaries can be
reconciled with current accretion torque models. We perform a statistical
analysis of the spin distributions and show that there is evidence for two
sub-populations among low-mass X-ray binaries, one at relatively low spin
frequency, with an average of ~300 Hz and a broad spread, and a peaked
population at higher frequency with average spin frequency of ~575 Hz. We show
that the two sub-populations are separated by a cut-point at a frequency of
~540 Hz. We also show that the spin frequency of radio millisecond pulsars does
not follow a log-normal distribution and shows no evidence for the existence of
distinct sub-populations. We discuss the uncertainties of different accretion
models and speculate that either the accreting neutron star cut-point marks the
onset of gravitational waves as an efficient mechanism to remove angular
momentum or some of the neutron stars in the fast sub-population do not evolve
into radio millisecond pulsars.
