  To estimate the feasibility of dense-matter phase transition, we studied the
evolution of the central density as well as the baryon chemical potential of
accreting neutron stars. We compared the thin-disk accretion with and without
the magnetic field torque with the spin-down scenario for a selection of recent
equations of state. We compared the prevalent (in the recycled-pulsar context)
Keplerian thin-disk model, in which the matter is accreted from the
marginally-stable circular orbit, with the recent magnetic-torque model that
takes into account the influence of stellar magnetic field on the effective
inner boundary of the disk. Calculations were performed using a multi-domain
spectral methods code in the framework of General Relativity. We considered
three equations of state consistent with the recently measured mass of PSR
J1614-2230, 1.97 +- 0.04 M_sun (one of them softened by the appearance of
hyperons). If there is no magnetic torque and efficient angular momentum
transfer from the disk to the star, substantial central compression is limited
to the region of initial stellar masses close to the maximum mass. Outside the
maximum mass vicinity, accretion-induced central compression is significant
only if the angular momentum transfer is inefficient. Accounting for the
magnetic field effectively decreases the efficiency of angular momentum
transfer and implies a significant central compression. An efficient angular
momentum transfer from a thin disk onto a non-magnetized neutron star does not
provide a good mechanism for the central compression and possible phase
transition. Substantial central compression is possible for a broad range of
masses of slowly-rotating initial configurations for magnetized neutron stars.
Accretion-induced central compression is particularly strong for stiff equation
of state with a high-density softening.
