Ordering energy levels of interacting spin systems

The total spin S is a good quantum number in problems of interacting spins. We have shown that for rather general antiferromagnetic or ferrimagnetic Hamiltonians, which need not exhibit translational invariance, the lowest energy eigenvalue for each value of S [denoted E(S)] is ordered in a natural way. In antiferromagnetism, E(S + 1) > E(S) for S ≥ 0. In ferrimagnetism, E(S + 1) > E(S) for S ≥ script S sign, and in addition the ground state belongs to S ≤ script S sign. script S sign is defined as follows: Let the maximum spin of the A sublattice be SA and of the B sublattice SB; then script S sign ≡ |SA - SB|. Antiferromagnetism is treated as the special case of script S sign = 0. We also briefly discuss the structure of the lowest eigenfunctions in an external magnetic field.