Abstract
New exactly solvable SO(q)-invariant q-state vertex models are introduced. We employ a new method using inversion relations which enables us to determine directly the spectra of the transfer matrices. The results are applied to related quantum spin chains. A special case is the pure biquadratic spin-1 Hamiltonian which turns out to be noncritical. Various quantities are calculated, e.g., the energy gap and the correlation length.
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