  Accreting pulsars power relativistic jets, and display a complex spin
phenomenology. These behaviours may be closely related to the large-scale
configuration of the star's magnetic field, shaped by its interaction with the
surrounding accretion disc. Here we present the first relativistic simulations
of the interaction of a pulsar magnetosphere with an accretion flow. Our
axisymmetric simulations treat the magnetospheric, or coronal, regions using a
resistive extension of force-free electrodynamics. The magnetic field is also
evolved inside the disc, which is a defined volume with a specified velocity
field and conductivity profile, found using an alpha-disc model. We study a
range of disc alpha-parameters, thicknesses, magnetic Prandtl numbers, and
inner truncation radii. We find that a large fraction of the magnetic flux in
the pulsar's closed zone is opened by the intrusion of the disc, leading to an
enhancement of the power extracted by the pulsar wind and the spin-down torque
applied to the pulsar. In our simulations, most of the spin-down contribution
to the stellar torque acts on open field lines. The efficiency of field-line
opening is high in the simulations' long-term quasi-steady states, which
implies that a millisecond pulsar's electromagnetic wind could be strong enough
to power the observed neutron-star radio jets, and may significantly affect the
pulsar's spin evolution.
