Numerical studies of Ising spin glasses in two, three and four dimensions.

We present the results of numerical simulations on Ising spin glasses in zero magnetic field with nearest neighbor interactions on cubic lattices in two, three and four dimensions with both Gaussian and and +- J 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 T sub c = O, and obtain the correlation length exponent nu, and the exponent eta, at the zero temperature transition for the +- J model. In d = 3 we concentrate on results for the Gaussian distribution, since our results for the +-J distribution have been presented earlier. As expected, we find similar results for the two distributions, namely a non-zero T sub c 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 T sub c is non-zero with a long range ordered phase below T sub c. Our estimates for critical exponents in d = 4 agree well with results from recent high temperature series expansions.