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The integrability condition of the Ising model is understood as the SU(2)integrability condition and also as the model parameterized by the ellipticfunction, where the integrability condition is understood as the additiontheorem of the elliptic function. The generalization of this integrabilitycondition is to find the solution of the higher rank Lie group integrabilitycondition and also to find the model parameterized by higher genushyperelliptic function. For the preparation of this purpose, we give theexplicit formula of the addition formula for g = 2 hyperelliptic function.

Integrability Condition in the Statistical Model and the Addition Formula of g = 2 Hyperelliptic Function