| The number of ground states of a classical Edwards-Anderson ±J spin glass grows exponentially with system size. We present an efficient and exhaustive algorithm for finding all of the ground states of the two-dimensional system and analyze the log-normal distribution of these ground states. We also investigate how small perturbations to the Hamiltonian break this huge degeneracy. We characterize the ground states of a system with a weak quantum tunneling term. Finally, we describe a natural way to group sets of ground states together and its physical implications. |
