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arXiv:hep-th/0008085 · Nuclear Physics B

Some exact results for the three-layer Zamolodchikov model

Herman E. Boos, Vladimir V. Mangazeev

Published Jan 1, 2001• 2 citations
arXivHTMLPDF
DOI
10.1016/s0550-3213(00)00619-2

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In this talk, we present our recent results on the three-layer Zamolodchikov model. We discuss solutions to the Bethe ansatz equations following from functional relations. We consider two regimes I and II that differ by the signs of the spherical sides ( a 1 , a 2 , a 3 ) → (− a 1 , − a 2 , − a 3 ). Also, we accept the two-line hypothesis for regime I and the one-line hypothesis for regime II. In the thermodynamic limit, we derive integral equations for distribution densities and solve them exactly. Using this solution, we calculate the partition function for the three-layer Zamolodchikov model and check the compatibility of this result with functional relations. We also discuss the reasons for the discrepancy with Baxter’s result of 1986.
Evidence is presented in favour of the hypothesis that the Zamolodchikov model (an exactly solvable three-dimensional lattice model without any temperature-like parameters) is critical. The evidence is obtained by generalising the Zamolodchikov model to include a temperature-like variable. The magnetisation curve of this model is then studied using a modified form of a variational approximation formulated earlier. Also the authors show the two-layer Zamolodchikov model corresponds to a critical free-fermion model.