Physics – Condensed Matter – Superconductivity
Scientific paper
2003-06-05
J. Phys. Cond. Matt., 15, 4583 (2003)
Physics
Condensed Matter
Superconductivity
to appear in J. Phys. Cond. Matt
Scientific paper
10.1088/0953-8984/15/26/308
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 $ - {3 \pi \over 4} < \gamma < - {\pi \over 2}$ belongs to total spin $S_{\rm tot} = 0$, whereas the state of minimum excited energy but with finite $S_{\rm tot}$ belongs to $S_{\rm tot} = 2$. These results are constrasted with the generalized Marshall theorems, applicable to a bipartite lattice and $ - {\pi \over 2} < \gamma \le 0$.
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