  Orbital magnetism in an integrable model of a multichannel ring with
long-ranged electron-electron interactions is investigated. In a noninteracting
multichannel system, the response to an external magnetic flux is the sum of
many diamagnetic and paramagnetic contributions, but we find that for
sufficiently strong correlations, the contributions of all channels add
constructively, leading to a parity (diamagnetic or paramagnetic) which depends
only on the total number of electrons. Numerical results confirm that this
parity-locking effect is robust with respect to subband mixing due to disorder.
