Centre for Mathematics and its Applications,

Some exact results for the three-layer Zamolodchikov model. Abstract In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works [18] and [19]. We analyse numerically the solutions to the Bethe ansatz equations obtained in [19]. We consider two regimes I and II which differ by the signs of the spherical sides (a 1 , a 2 , a 3) → (−a 1 , −a 2 , −a 3). 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 obtained in [19]. We also do some numeric checkings of our results.