It is shown that the Zamolodchikov model on the cubic lattice of $N$ sites is equivalent to a spin model on a lattice of $2N$ sites with just two-spin and three-spin interactions. Together with the known transfer-matrix commutativity, this implies that the partition function $Z$ (for $N$ large) factors into a product of single-variable functions. These functions, and hence $Z$ , are calculated by using symmetry relations. The model appears to be a critical free-fermion model.It is shown that the Zamolodchikov model on the cubic lattice of $N$ sites is equivalent to a spin model on a lattice of $2N$ sites with just two-spin and three-spin interactions. Together with the known transfer-matrix commutativity, this implies that the partition function $Z$ (for $N$ large) factors into a product of single-variable functions. These functions, and hence $Z$, are calculated by using symmetry relations. The model appears to be a critical free-fermion model.

Physical Review LettersNov 5, 198421 citations

The free energy of the three-dimensional Zamolodchikov model

M. L. Glasser

Details are given for the reduction of Baxter’s expression for the exact partition function per site of the Zamolodchikov model to explicit form.

Journal of Mathematical PhysicsNov 1, 19860 citations

Some exact results for the three-layer zamolodchikov model

Herman E. Boos, Vladimir V. Mangazeev

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.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.

Physics of Atomic NucleiJun 1, 20020 citations

Partition function zeros for the two-dimensional Ising model III

John Stephenson, Jan Van Aalst

Physica A Statistical Mechanics and its ApplicationsMay 1, 198620 citations

It is shown that the Zamolodchikov model on the cubic lattice of

N

sites is equivalent to a spin model on a lattice of

2N

sites with just two-spin and three-spin interactions. Together with the known transfer-matrix commutativity, this implies that the partition function

Z

(for

N

large) factors into a product of single-variable functions. These functions, and hence

Z

, are calculated by using symmetry relations. The model appears to be a critical free-fermion model.