Exact Results for a Spin-${\bf 1}$ lattice

We consider a lattice of spin-1 particles with a general pairwise interaction $ [ {\rm cos} \gamma ({\bf S}{l} \cdot {\bf S}{l+1}) \

{\rm sin} \gamma ({\bf S}{l} \cdot {\bf S}{l+1})^2
]$. We show that, for a large class of lattices with even number of sites, the ground state for the region $- \frac{3 π}{4} < γ < - \frac{π}{2}$ belongs to total spin $S_{t o t} = 0$ , whereas the state of minimum excited energy but with finite $S_{t o t}$ belongs to $S_{t o t} = 2$ . These results are constrasted with the generalized Marshall theorems, applicable to a bipartite lattice and $- \frac{π}{2} < γ \leq 0$ .

We consider a lattice of spin-1 particles with a general pairwise interaction $ [ {\rm cos} \gamma ({\bf S}{l} \cdot {\bf S}{l+1}) \

{\rm sin} \gamma ({\bf S}{l} \cdot {\bf S}{l+1})^2
]$. We show that, for a large class of lattices with even number of sites, the ground state for the region $- \frac{3 π}{4} < γ < - \frac{π}{2}$ belongs to total spin $S_{t o t} = 0$ , whereas the state of minimum excited energy but with finite $S_{t o t}$ belongs to $S_{t o t} = 2$ . These results are constrasted with the generalized Marshall theorems, applicable to a bipartite lattice and $- \frac{π}{2} < γ \leq 0$ .

Exact Results for a Spin- $1$ lattice