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 ± , where we find f + /f − = 2.06(1).

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We simulated the critical behavior of the d = 3 Ising model with surfaces with a cluster Monte Carlo method at the multicritical point and at the ordinary transition. The surface exponents Pi have been determined using finite-size scaling. The errors of the resulting values Pi = 0.2375(15) and Pi = 0.807(4) are an order of magnitude smaller than in previous determinations. Whereas the values of the exponents agree with the prediction of the e expansion, the universal ratios of susceptibility and magnetization amplitudes at the special transition are at variance with those predictions.

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