  We investigate the spin-spin correlation functions of Ising magnets at
complex values of the temperature, T. For one-dimensional chain and ladder
systems, we show the existence of a kind of helimagnetic order in the vicinity
of contours where the leading two eigenvalues of the transfer matrix become
equal in magnitude. We analyse the development of long-range order as the
two-dimensional limit is approached, and find that there is rich structure in
much of the complex-T plane. In particular, and contrary to the work of Fisher
on this problem, the development of long-range order is actually associated
with a proliferation of partition function zeros in a certain finite region of
that plane containing the real-temperature magnetically ordered phase. The
thermodynamic consequences of this are also discussed.
