How to evaluate ground-state landscapes of spin glasses thermodynamical correctly

Ground states of three-dimensional $\pm J$ Ising spin glasses are calculated for sizes up to 143 using a combination of a genetic algorithm and cluster-exact approximation. For each realization several independent ground states are obtained. Then, by applying ballistic search and T=0 Monte-Carlo simulations, it is ensured that each ground state appears with the same probability. Consequently, the results represent the true T=0 thermodynamic behavior. The distribution P(|q|) of overlaps is evaluated. For increasing size the width of P(|q|) and the fraction of the distribution below $q_0\equiv 0.5$ converge to zero. This indicates that for the infinite system P(|q|) is a delta function, in contrast to previous results. Thus, the ground-state behavior is dominated by few large clusters of similar ground states