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We consider several anisotropic extensions of the Belavin model, and showthat integrability holds also for the massive case for some specific relationsbetween the coupling constants. This is done by relating the S-matrixfactorization property to the exceptional solutions of the eight-vertex model.The relation of exceptional solutions to the XXZ and six-vertex models is alsoshown.

Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models