Classification of Exactly Solvable Two-Component Models

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Abstract
In the case of two-component models, all possible solutions for factorization equations of S-matrix are obtained. These solutions give a classification of solvable vertex models. It is found that Yang-Baxter relation is more general than the factorization equation. The six vertex model by Yang, Yang and Sutherland is derived not from the factorization equation but from Yang-Baxter relation. Thus it is concluded that Yang-Baxter relation lies at the basis of all the known solvable two component models. Furthermore, spin Hamiltonians corresponding to our vertex models are presented in explicit forms.

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