Correlation Function in Ising Models

Abstract

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 succesfully 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 $f_{\pm}$, where we find $f_+/f_-=2.06(1)$.