The Elliptic Function in Statistical Integrable Models

TL;DR

This paper explores the connection between SU(2) symmetry and elliptic functions in two-dimensional statistical integrable models, explaining why models like Ising and chiral Potts are integrable.

Contribution

It provides a group-theoretical explanation for the role of elliptic functions in the integrability of these models, linking symmetry to parametrization.

Findings

SU(2) symmetry underpins integrability in these models

Elliptic functions parametrically describe Boltzmann weights

The connection clarifies the mathematical structure of integrable models

Abstract

We examine the group theoretical reason why various two dimensional statistical integrable models, such as the Ising model, the chiral Potts model and the Belavin model, becomes integrable. The symmetry of these integrable models is SU(2) and the Boltzmann weight can be parametrized by the elliptic function in many cases. In this paper, we examine the connection between the SU(2) symmetry and the elliptic function in the statistical integrable models.