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A neutron star in binary orbit with a low-mass non-degenerate companionbecomes a source of x-rays with millisecond variability when mass accretionspins it up. Centrifugally driven changes in density profile may initiate aphase transition in a growing region of the core parallel to what may takeplace in an isolated millisecond pulsar, but in reverse. Such a star will spenda longer time in the spin frequency range over which the transition occurs thanelsewhere because the change of phase, paced by the spinup rate, is accompaniedby a growth in the moment of inertia. The population of accreters will exhibita clustering in the critical frequency range. A phase change triggered bychanging spin and the accompanying adjustment of moment of inertia has itsanalogue in rotating nuclei.Comment: 5 pages (AIPproc latex) 6 figures. To be presented at the  International Conference on Nuclear Physics, 30 July - 3 August 2001,  Berkeley, Californi

Spin clustering of accreting X-ray neutron stars as possible evidence of quark matter