  In the theory of the two-dimensional Ising model, the diagonal susceptibility
is equal to a sum involving Toeplitz determinants. In terms of a parameter k
the diagonal susceptibility is analytic inside the unit circle, and the authors
proved the conjecture that this function has the unit circle as a natural
boundary. The symbol of the Toepltiz determinants was a k-deformation of one
with a single singularity on the unit circle. Here we extend the result, first,
to deformations of a larger class of symbols with a single singularity on the
unit circle, and then to deformations of (almost) general Fisher-Hartwig
symbols.
