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

TL;DR

This paper explores the integrability conditions of the Ising model through elliptic and hyperelliptic functions, providing explicit formulas for genus 2 hyperelliptic addition formulas to generalize the model's integrability.

Contribution

It introduces explicit addition formulas for genus 2 hyperelliptic functions, extending the understanding of integrability conditions beyond elliptic functions.

Findings

Explicit formula for g=2 hyperelliptic addition theorem

Connection between integrability conditions and hyperelliptic functions

Framework for higher genus hyperelliptic integrability

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.