Critical Spin Models with Continuously Varying Exponents

The eigenenergies for the spin $S$ generalization of the critical $\mathrm{XXZ}$ model are calculated by solving numerically, for finite chains, their associated Bethe-Ansatz equations. The conformal anomaly and scaling dimensions are obtained from the conformal invariance of the infinite chain. Our results reveal that these models are governed by a conformal field theory with central charge $c=\frac{3S}{\mathrm{}(S+1\mathrm{})\mathrm{}}$ and having continuously varying critical exponents, like the eight-vertex model. We also show that they are related to a large class of unitary conformal field theories.