Antiferromagnetic order and frustration in small clusters

Magnetic properties of small antiferromagnetic clusters are studied within the framework of the nearest-neighbor Ising model. We analyze in detail several cluster geometries with different lattice structures and examine the competing effects due to antiferromagnetic order, frustration, and external field. For some geometries in the presence of an external magnetic field, magnetization is found to increase with increasing temperature in a considerable temperature range. We also consider conditions under which antiferromagnetic clusters can display superparamagnetic behavior. In general, magnetization is found to depend strongly on the lattice structure of the cluster, but to be rather insensitive to local modifications of the coupling strength. The approach towards the bulk properties for increasing cluster size and the possibility of deducing the lattice structure from the observed magnetic behavior are discussed.