Defect energies of two-, three- and four-dimensional Ising spin glasses

Abstract

The defect energies of Ising spin systems with nearest-neighbour interactions whose strengths are normally distributed, have been investigated numerically for square, cubic and hypercubic lattices. In four dimensions the defect energy is independent of the size of the system only when the bonds are distributed with zero mean, but in two and three dimensions the defect energy is independent of the system size for all values of the mean less than a certain critical value. This provides further evidence that four dimensions is the dimensionality below which Edwards-Anderson order cannot exist at non-zero temperatures.