  We study analytically the effect of a correlated random potential on the
persistent current in a one-dimensional ring threaded by a magnetic flux
$\phi$, using an Anderson tight-binding model. In our model, the system of
$N=2M$ atomic sites of the ring is assumed to be partitioned into $M$ pairs of
identical nearest-neighbour sites (dimers). The site energies for different
dimers are taken to be uncorrelated gaussian variables. For this system we
obtain the exact flux-dependent energy levels to second order in the random
site energies, using an earlier exact transfer matrix perturbation theory.
These results are used to study the mean persistent current generated by
$N_e\leq N$ spinless electrons occupying the $N_e$ lowest levels of the
flux-dependent energy band at zero temperature. Detailed analyses are carried
out in the limit $1\ll N_e\ll N$ and for a half-filled band ($N_e=N/2$), for
magnetic fluxes $-1/2 <\phi/\phi_0<1/2$. While the uncorrelated disorder leads
to a reduction of the persistent current, the disorder correlation acts to
enhance it. In particular, in the half-filled band case the correlated disorder
leads to a global flux-dependent enhancement of persistent current which has
the same form for even and odd $N_e$. At low filling of the energy band the
effect of the disorder on the persistent current is found to depend on the
parity of $N_e$: the correlated disorder yields a reduction of the current for
odd $N_e$ and an enhancement of the current for even $N_e$.
