  We study the spin-spin correlation function in or near the T=0 ground state
of the antiferromagnetic Ising model on a triangular lattice. At zero
temperature its modulation on the sublattices gives rise to two Bragg peaks in
the structure factor, and a known expression for the algebraic decay of
correlations enables us to examine the form of the diffusive scattering. We do
so by means of a comparison between exact results and data calculated using
standard Monte Carlo techniques. At non-zero temperatures the finite
correlation length alters this form, and we account for the change by proposing
a generalisation of the zero temperature pair correlation function. The size
dependence of our simulation data is investigated through a novel finite-size
scaling analysis where t = exp(-2/T) is used as the temperature parameter.
