The ground state energy of the Edwards-Anderson Ising spin glass with a hybrid genetic algorithm

Ground states of three-dimensional Edwards-Anderson ±J Ising spin glasses were calculated with a hybrid of genetic algorithm and local optimization. The algorithm was fast and reliable enough to allow extensive calculations for systems of linear size between 3 and 14 and determination of the average ground state energies with small errors. A linear dependence on 1/volume approximates the data very accurately in the whole range. The −1.7863 ± 0.0004 value for the ground state energy per spin of the infinite system was determined with extrapolation. The main source of uncertainty is that the functional form of the small but significant deviation from the linear 1/volume dependence is unknown.