The Order Parameter of the Chiral Potts Model

An outstanding problem in statistical mechanics is the order parameter of the chiral Potts model. An elegant conjecture for this was made in 1983. It has since been successfully tested against series expansions, but there is as yet no proof of the conjecture. Here we show that if one makes a certain analyticity assumption similar to that used to derive the free energy, then one can indeed verify the conjecture. The method is based on the ‘‘broken rapidity line’’ approach pioneered by Jimbo et al. (J. Phys. A 26:2199--2210 (1993).).