Some exact results for the three-layer Zamolodchikov model

TL;DR

This paper advances the understanding of the three-layer Zamolodchikov model by deriving exact solutions for its partition function through analysis of Bethe ansatz equations in different regimes.

Contribution

It provides the first exact solutions for the partition function of the three-layer Zamolodchikov model using integral equations and numerical validation.

Findings

Derived integral equations for distribution densities in regimes I and II.

Obtained exact partition function expressions in the thermodynamic limit.

Confirmed compatibility of results with functional relations.

Abstract

In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works. We analyse numerically the solutions to the Bethe ansatz equations. We consider two regimes I and II which differ by the signs of the spherical sides (a1,a2,a3)->(-a1,-a2,-a3). We accept the two-line hypothesis for the regime I and the one-line hypothesis for the regime II. In the thermodynamic limit we derive integral equations for distribution densities and solve them exactly. We calculate the partition function for the three-layer Zamolodchikov model and check a compatibility of this result with the functional relations. We also do some numerical checkings of our results.