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We present the results of numerical simulations on Ising spin glasses in zero magnetic field with nearest-neighbor interactions on hyper-cubic lattices in two, three, and four dimensions with both Gaussian and bond distributions. Finite-size scaling is used to analyze the results. In two dimensions (d=2) we agree with earlier work that the transition temperature is at T₂=0, and obtain the correlation-length exponent, and the exponent, at the zero-temperature transition for the model. In d=3 dimensions we concentrate on results for the Gaussian distribution, since our results for the distribution have been presented earlier. As expected, we find similar results for the two distributions, namely a nonzero T₂ but evidence that d=3 is close to the lower critical dimension. In a four-dimensional spin glass with Gaussian bonds we find that only a modest amount of computer time is required to show that T₂ is nonzero with a long-range-ordered phase below T₂. Our estimates for critical exponents in d=4 dimensions agree well with results from recent high-temperature-series expansions.
Bhatt et al. (1988) studied this question.