Partition Function of the Three-Dimensional Zamolodchikov 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.