  We study the zero-bandwidth limit of the two-impurity Anderson model in an
antiferromagnetic (AF) metal. We calculate, for different values of the model
parameters, the lowest excitation energy, the magnetic correlation
$<\mathbf{S}_{1}\mathbf{S}_{2}>$ between the impurities, and the magnetic
moment at each impurity site, as a function of the distance between the
impurities and the temperature. At zero temperature, in the region of
parameters corresponding to the Kondo regime of the impurities, we observe an
interesting competition between the AF gap and the Kondo physics of the two
impurities. When the impurities are close enough, the AF splitting governs the
physics of the system and the local moments of the impurities are frozen, in a
state with very strong ferromagnetic correlation between the impurities and
roughly independent of the distance. On the contrary, when the impurities are
sufficiently far apart and the AF gap is not too large, the scenario of the
Kondo physics take place: non-magnetic ground state and the possibility of
spin-flip excitation emerges and the ferromagnetic
$<\mathbf{S}_{1}\mathbf{S}_{2}>$ decreases as the distance increases, but the
complete decoupling of the impurities never occurs. In adition, the presence of
the AF gap gives a non-zero magnetic moment at each impurity site, showing a
non complete Kondo screening of the impurities in the system. We observe that
the residual magnetic moment decreases when the distance between the impurities
is increased.
