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

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