  In this paper, we prove that any translation and $SU_2(\IC)$-invariant pure
state of $\IM=\otimes_{k \in \IZ}\!M^{(k)}_d(\IC)$, that is also real, lattice
symmetric and reflection positive with a certain twist $r_0 \in U_d(\IC)$, is
finitely correlated and its two-point spatial correlation function decays
exponentially whenever $d$ is an odd integer. In particular, the Heisenberg
iso-spin anti-ferromagnetic integer spin model admits unique low temperature
limiting ground state and its spatial correlation function decays
exponentially. The unique low temperature limiting ground state of the
Hamiltonian is determined by the unique solution to Clebsch-Gordon
inter-twinning isometry between two representations of $SU_2(\IC)$.
