EXACT GROUND-STATE SPIN CONFIGURATIONS FOR 2D AND 3D LATTICES WITH NEAREST-NEIGHBOR BILINEAR EXCHANGE

A systematic research of the bilinear exchange Hamiltonians providing an exactly known ground state spin configuration is performed for two and three dimensional lattices. Apart from the well known ferromagnetic Heisenberg and ferro or antiferromagnetic Ising systems, particular attention is paid to the anisotropic Heisenberg model H-ij = - J(x) S-ix S-jx - Jy S-iy S-jy - J(z) S-iz S-jz for a bond along the z axis. It is shown that, under special conditions, this pair interaction leads to a two sublattice antiferromagnetic configuration which is an eigenstate of the system at T = 0 K, i.e. without spin deviation. All the possible structures displaying this remarkable property are derived.