  The accretion induced neutron star magnetic field evolution is studied
through considering the accretion flow to drag the field lines aside and dilute
the polar field strength, and as a result the equatorial field strength
increases and is buried inside the crust. The main conclusions of model are as
follows: (i) the polar field decays with increasing the accreted mass; (ii) The
bottom magnetic field strength of about $10^8$ G can occur when neutron star
magnetosphere radius approaches the star radius, which depends on the accretion
rate as $\mdot^{1/2}$; (iii) The neutron star magnetosphere radius decreases
with accretion until it reaches the star radius, and its evolution is little
influenced by the initial field and the accretion rate after accreting $\sim
0.01 \ms$, which implies that the magnetosphere radii of neutron stars in LMXBs
would be homogeneous for Z sources and Atoll sources if they accreted the
comparable masses. As an extension, the physics effects of the possible strong
magnetic zone in the X-ray neutron stars and recycled pulsars are discussed.
Moreover, The strong magnetic fields in the binary pulsars PSR 1831-00 and PSR
1718-19 after accreting about half solar mass in the binary accretion phase,
$8.7\times10^{10}$ G and $1.28\times10^{12}$ G, respectively, can be explained
through considering the incomplete frozen flow in the polar zone. As a model's
expectation, the existence of the low magnetic field ($\sim 3\times 10^{7}$ G)
neutron stars or millisecond pulsars is suggested.
