Numerical analysis of magnetic states mixing in the Heisenberg model with the dihedral symmetry

The total spin number S is not a ‘good quantum number for’ the Heisenberg model with singleion anisotropy, so the Hamiltonian eigenstates with different S may form linear combinations. Sometimes it is assumed that S can be used as an ‘approximate quantum number’, though some results show that mixing of S-states is important in investigations of magnetic molecules. Some small spin systems with the dihedral symmetry are analyzed to investigate different schemes of mixing and its dependence on the anisotropy parameter. The results show various behavior of the magnetic state mixing. The mean (over a state) value of total spin is quite stable for the ground state, but in other cases this dependence is nonlinear and sometimes non-monotonic