Scaling of stiffness energy for three-dimensional±JIsing spin glasses

Large numbers of ground states of three-dimensional (3D) Edwards-Anderson Ising spin glasses are calculated for sizes up to ${10}^3$ using a combination of a genetic algorithm and cluster-exact approximation. A detailed analysis shows that true ground states are obtained. The ground-state stiffness (or domain wall) energy Δ is calculated. A $|\Delta |\sim L^{{\Theta }_S}$ behavior with ${\Theta }_S=0.19\mathrm{}\left(2\right)\mathrm{}$ is found that strongly indicates that the 3D model has an equilibrium spin-glass-paramagnet transition for nonzero $T_c.$