  We investigate the ground state structure of the three-dimensional Ising spin
glass in zero field by determining how the ground state changes in a fixed
finite block far from the boundaries when the boundary conditions are changed.
We find that the probability of a change in the block ground state
configuration tends to zero as the system size tends to infinity. This
indicates a trivial ground state structure, as predicted by the droplet theory.
Similar results are also obtained in two dimensions.
