Some exact results for the three-layer Zamolodchikov model Original Research Article

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 (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 obtained in H.E. Boos, V.V. Mangazeev, J. Phys. A 32 (1999) 5285–5298. We also do some numeric checkings of our results.