Bethe Ansatz Equations for the Broken $Z_{N}$-Symmetric Model

TL;DR

This paper derives Bethe Ansatz equations for an elliptic off-critical extension of the Fateev-Zamolodchikov model with broken Z_N symmetry, enabling calculation of its free energy.

Contribution

It introduces a new set of Bethe Ansatz equations for the broken Z_N-symmetric model using transfer matrix functional relations.

Findings

Derived Bethe Ansatz equations for the model.

Calculated free energy based on the string hypothesis.

Extended understanding of off-critical elliptic models.

Abstract

We obtain the Bethe Ansatz equations for the broken ${\bf Z}_{N}$-symmetric model by constructing a functional relation of the transfer matrix of $L$-operators. This model is an elliptic off-critical extension of the Fateev-Zamolodchikov model. We calculate the free energy of this model on the basis of the string hypothesis.