Ordering Energy Levels of Interacting Spin Systems

@article{Lieb1962OrderingEL,
  title={Ordering Energy Levels of Interacting Spin Systems},
  author={Elliott H. Lieb and Daniel Charles Mattis},
  journal={Journal of Mathematical Physics},
  year={1962},
  volume={3},
  pages={749-751}
}
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 > O. In ferrimagnetism, E(S + 1) > E(S) for S > S, and in addition the ground state belongs to S < S. S is defined as follows: Let the maximum spin… 
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