Small clusters with anisotropic antiferromagnetic exchange in a magnetic field

We consider small symmetric clusters of magnetic atoms (spins) with anisotropic exchange interaction between the atoms in a magnetic field at zero temperature. The inclusion of the anisotropy leads to a wealth of different phases as a function of the applied magnetic field. These are not phases in the thermodynamic sense with critical properties but rather physical structures with different arrangements of the spins and hence different symmetries. We study the spatial symmetry of these phases, for the classical and quantum cases. Results are presented mainly for three frustrated systems, the triangle, the tetrahedron and the five-atom ring, which have many interesting features. In the class…