  For the Ising model, the calculation of the spontaneous magnetization leads
to the problem of evaluating a determinant. Yang did this by calculating the
eigenvalues in the large-lattice limit. Montroll, Potts and Ward expressed it
as a Toeplitz determinant and used Szego's theorem: this is almost certainly
the route originally travelled by Onsager. For the corresponding problem in the
superintegrable chiral Potts model, neither approach appears to work: here we
show that the determinant D_PQ can be expressed as that of a product of two
Cauchy-like matrices. One can then use the elementary exact formula for the
Cauchy determinant. One of course regains the known result, originally
conjectured in 1989.
