Small clusters with Heisenberg antiferromagnetic exchange

We study small symmetrical clusters of magnetic ions with Heisenberg anti-f erromagnetic exchange interaction. We calculate the magnetization and the s pecific heat as functions of applied magnetic field at zero and non-zero te mperature. Results are given for both classical and quantum systems. At zer o temperature the classical systems undergo a series of transitions where t he symmetry changes as a function of applied field. The quantum systems sho w similar features to Ising systems previously studied.