  We study four spins on a ring coupled through competing Heisenberg
interactions between nearest neighbors, $J$, and next-nearest neighbors,
$J_2\equiv\alpha J>0$. The spectrum is obtained in a simple way by using the
rules for addition of 4 angular momenta. This allows us to follow the evolution
of the ground state with $\alpha$, characterized by level crossings and by
analyses of spin-spin correlation functions. Further insight is obtained by
examining the entanglement between different parts of the system: we observe
that the entanglement entropy is strongly dependent on how the system is
partitioned.
