Small antiferromagnetic spin systems-Sublattice Hamiltonians

A few examples of four-spin Heisenberg systems with dominant antiferromagnetic couplings are considered. All systems can be described by the so-called sublattice Hamiltonian H=SA.SB or its modifications, where SX is the total spin of a sublattice X=A, B. In such a case (eigen)energies are simple functions of the total spin number S, total spins of sublattices SA, SB, and the Hamiltonian parameters (ratios of exchange integrals). Moreover, eigenstates are strictly determined by a coupling scheme assumed and the appropriate Clebsch-Gordan coefficients. In this sense the systems considered are classical ones.