  We discuss the implications of studies of partition function zeros and
equimodular curves for the analytic properties of the Ising model on a square
lattice in a magnetic field. In particular we consider the dense set of
singularities in the susceptibility of the Ising model at $H=0$ found by Nickel
and its relation to the analyticity of the field theory computations of Fonseca
and Zamolodchikov.
