Eight-vertex model in lattice statistics and one-dimensional anisotropic heisenberg chain. II. Equivalence to a generalized ice-type lattice model

We establish an equivalence between the zero-field eight-vertex model and an Ising model (with four-spin interaction) in which each spin has L possible values, labeled 1, …, L, and two adjacent spins must differ by one (to modulus L). Such an Ising model can also be thought of as a generalized ice-type model and we will later show that the eigenvectors of the transfer matrix can be obtained by a Bethe-type ansatz.