Correlation function in Ising models

We simulated the Fourier transform of the correlation function of the Ising model in two and three dimensions using a single cluster algorithm with improved estimators. The simulations are in agreement with series expansion and the available exact results in d = 2, which shows, that the cluster algorithm can successfully be applied for correlations. We show as a further result that our data do not support a hypothesis of Fisher that in any d = 2 lattice the Fourier transform of the correlation function depends on the lattice generating function only. In d = 3 our simulation are again in agreement with the results from the series expansion, except for the amplitudes f±, where we find f+f- = 2.06(1).