  Exact diagonalization calculations reveal that the energy spacing $\Delta$ in
the conduction band tunes the interplay between the {\it local} Kondo and {\it
non local} RKKY interactions, giving rise to a "Doniach phase diagram" for a
nanocluster with regions of prevailing Kondo or RKKY correlations. The parity
of the total number of electrons alters the competition between the Kondo and
RKKY correlations. This interplay may be relevant to experimental realizations
of small rings or quantum dots with tunable magnetic properties. Below a
critical value V$_c$ of the hybridization the susceptibility exhibits a low-T
exponential activation behavior determined by the interplay of the spin gap and
$\Delta$.
