Derivation of the Order Parameter of the Chiral Potts Model

We derive the order parameter of the chiral Potts model, using the method of Jimbo et al. The result agrees with previous conjectures.

Figure 1

The square lattice with the cut rapidity line below $a$.

Figure 2

The $t_p$ plane for $N=3$, showing the cuts ${\mathcal{C}}_0$, ${\mathcal{C}}_1$, ${\mathcal{C}}_2$.