  We use a large set of state-of-the-art cosmological N-body simulations [512^3
particles] to study the intrinsic ellipticity correlation functions of halos.
With the simulations of different resolutions, we find that the ellipticity
correlations converge once the halos have more than 160 members. For halos with
fewer members, the correlations are underestimated, and the underestimation
amounts to a factor of 2 when the halos have only 20 particles. After
correcting for the resolution effects, we show that the ellipticity
correlations of halos in the bigger box (L=300 mpc) agree very well with those
obtained in the smaller box (L=100 mpc). Combining these results from the
different simulation boxes, we present accurate fitting formulae for the
ellipticity correlation function c_{11}(r) and for the projected correlation
functions Sigma_{11}(r_p) and Sigma_{22}(r_p) over three orders of magnitude in
halo mass. The latter two functions are useful for predicting the contribution
of the intrinsic correlations to deep lensing surveys. With reasonable
assumptions for the redshift distribution of galaxies and for the mass of
galaxies, we find that the intrinsic ellipticity correlation can contribute
significantly not only to shallow surveys but also to deep surveys. Our results
indicate that previous similar studies significantly underestimated this
contribution for their limited simulation resolutions.
