On solving the Ising model functional relation without elliptic functions

The exactly solvable N-state chiral Potts model differs from previous solvable lattice models in that its mathematics leads to hyperelliptic rather than ordinary elliptic functions. It is still an open question whether these hyperelliptic functions provide a useful computational tool: in particular, it has recently been shown that the functional relation for the eigenvalues of the transfer matrix can be solved directly, without introducing such functions. When N = 2 the model reduces to the Ising model and this method provides a novel and straightforward way of solving the Ising model. In fact the method simplifies considerably: here we present the resulting technique.