The derivation of the free energy of the ising model from that of the eight-vertex model

The zero-field eight-vertex model is equivalent to a square lattice Ising model, with a four-spin coupling and second neighbour coupling but no nearest neighbour coupling. When the four-spin coupling is zero, the model reduces to two decoupled nearest neighbour Ising models. The standard formula for the free energy of the Ising model is, therefore, implicit in Baxterʹs expression for the free energy of the zero-field eight-vertex model. The detailed derivation of this result has not appeared in print. As a footnote to Baxterʹs work this paper provides the necessary analysis.