  The inner regions of accretion disks of weakly magnetized neutron stars are
affected by general relativity and stellar magnetic fields. Even for field
strengths sufficiently small so that there is no well-defined magnetosphere
surrounding the neutron star, there is still a region in the disk where
magnetic field stress plays an important dynamical role. We construct magnetic
slim disk models appropriate for neutron stars in low-mass X-ray binaries
(LMXBs) which incorporate both effects (GR and magnetic fields). The
B-field--disk interaction is treated in a phenomenological manner, allowing for
both closed and open field configurations. We show that even for surface
magnetic fields as weak as $10^7-10^8$ G, the sonic point of the accretion flow
can be significantly modified from the pure GR value (near $6M$). We derive an
approximate analytical expression for the sonic radius and show that it mainly
depends on the surface field strength $B_0$ and mass accretion rate $\dot M$
through the ratio $b^2\propto B_0^2/\dot M$. The sonic radius thus obtained
approaches the usual Alfven radius for high $b^2$, and asymptotes to $6M$ as
$b^2\to 0$. We therefore suggest that for neutron stars in LMXBs, the
distinction between the disk sonic radius and the magnetospheric radius may not
exist. We apply our theoretical results to the kHz QPOs observed in the X-ray
fluxes of LMXBs. If these QPOs are associated with the orbital frequency at the
inner radius of the disk, then the QPO frequencies and their correlation with
mass accretion rate can provide useful constraints on the nature of the
magnetic field -- disk interactions as well as on the structure of magnetic
fields in LMXBs. Current observational data may suggest that the magnetic
fields in LMXBs have complex topology.
