  We present the results of extensive Monte Carlo simulations of Ising models
with algebraically decaying ferromagnetic interactions in the regime where
classical critical behavior is expected for these systems. We corroborate the
values for the exponents predicted by renormalization theory for systems in
one, two, and three dimensions and accurately observe the predicted logarithmic
corrections at the upper critical dimension. We give both theoretical and
numerical evidence that above the upper critical dimension the decay of the
critical spin-spin correlation function in finite systems consists of two
different regimes. For one-dimensional systems our estimates for the critical
couplings are more than two orders of magnitude more accurate than existing
estimates. In two and three dimensions we give, to our knowledge, the first
results for the critical couplings.
