We study the evolution of the rotation frequency for accreting compact star
s. The discontinuous change of the moment of inertia of a rapidly rotating
star due to the possible quark core appearance entails a characteristic cha
nge in the spin evolution. Numerical solutions have been performed using a
model equation of state describing the deconfinement phase transition. Traj
ectories of spin evolution are discussed in the angular velocity-baryon num
ber plane (phase diagram) for different accretion scenarios defined by the
initial values of mass and magnetic field of the star as well as mass accre
tion rate and magnetic field decay time. We observe a characteristic increa
se in the waiting time when a configuration enters the quark core regime. O
verclustering of the population of Z sources of low-mass X-ray binaries in
the phase diagram is suggested as a direct measurement of the critical line
for the deconfinement phase transition since it is related to the behavior
of the moment of inertia of the compact star.