  We demonstrate that a split-gate quantum wire in the integer quantum Hall
regime can exhibit electronic transport hysteresis for up- and down-sweeps of a
magnetic field. This behavior is shown to be due to phase spin transitions
between two different ground states with and without spatial spin polarization
in the vicinity of the wire boundary. The observed effect has a many-body
origin arising from an interplay between a confining potential, Coulomb
interactions and the exchange interaction. We also demonstrate and explain why
the hysteretic behavior is absent for steep and smooth confining potentials and
is present only for a limited range of intermediate confinement slopes.
