Calculation of ground states of four-dimensional±JIsing spin glasses

Ground states of four-dimensional $(d=4)$ Edwards-Anderson Ising spin glasses are calculated for sizes up to 7×7×7×7 using a combination of a genetic algorithm and cluster-exact approximation. The ground-state energy of the infinite system is extrapolated as e₀^∞=-2.095(1). The ground-state stiffness (or domain wall) energy Δ is calculated. A |Δ|~L^ΘS behavior with ΘS=0.64(5) is found which confirms that the $d=4$ model has an equilibrium spin-glass-paramagnet transition for nonzero Tc.