Exact results for a spin-1 lattice

We consider a lattice of spin-1 particles with a general pairwise interaction [(cosgamma)(S-l.Sl+1)+(singamma)(S-l.Sl+1)(2)]. We show that, for a large class of lattices with even numbers of sites, the ground state for the region -(3pi)/(4) < gamma < -(pi)/(2) has total spin S-tot = 0, whereas the state of minimum excited energy but with finite S-tot has S-tot = 2. These results are contrasted with the generalized Marshall theorems, applicable to a bipartite lattice and for -(pi)/(2) < gamma < 0.