Some exact results for the three-layer Zamolodchikov model

In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works (H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 3041-3054 and H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285-5298). We analyse numerically the solutions to the Bethe ansatz equations obtained in H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285-5298. 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 H.E. Boos, V,V. Mangazeev, J. Phys. A 32 (1999) 5285-5298, We also do some numeric checkings of our results. (C) 2001 Elsevier Science B.V. All rights reserved.