CLASSICAL CRITICAL-BEHAVIOR OF SPIN MODELS WITH LONG-RANGE INTERACTIONS

We present the results of extensive Monte Carlo simulations of Ising m odels with algebraically decaying ferromagnetic interactions in the re gime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalizati on theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections at the upper critical d imension. We give both theoretical and numerical evidence that above t he upper critical dimension the decay of the critical spin-spin correl ation function in finite systems consists of two different regimes. Fo r one-dimensional systems our estimates for the critical couplings are more than two orders of magnitude more accurate than existing estimat es. In two and three dimensions we are unaware of any other results fo r the critical couplings.