SERIES EXPANSIONS FOR THE ISING SPIN-GLASS IN GENERAL DIMENSION

We have developed 15th-order high-temperature series expansions for the study of the critical behavior of the Ising spin glass with nearest-neighbor exchange interactions each of which assumes the values +/- J randomly. Series for the Edwards-Anderson spin-glass susceptibility (chi-EA) and two of its derivatives with respect to the ordering field have been evaluated for hypercubic lattices in general dimension, d. These extend previous general-dimension series by five terms. Certain measureable universal amplitude ratios have been estimated from the new series. Accurate critical data for d = 5 and the first reliable estimates of the exponent-beta for d = 4 and 5, are given. We quote gamma = 1.73 +/- 0.03, 2.00 +/- 0.25, and 2.7(-0.6)+1.0 and beta = 0.95 +/- 0.04, 0.9 +/- 0.1, and 0.7 +/- 0.2 in 5, 4, and three dimensions, respectively. Our results provide a smooth extrapolation between the mean-field results above six dimensions and experiments and simulations in physical dimensions. We relate our calculated derivatives of chi-EA to measurements of derivatives of the magnetization with respect to a uniform magnetic field.