  The question of the number of thermodynamic states present in the
low-temperature phase of the three-dimensional Edwards-Anderson Ising spin
glass is addressed by studying spin and link overlap distributions using
population annealing Monte Carlo simulations. We consider overlaps between
systems with the same boundary condition-which are the usual quantities
measured-and also overlaps between systems with different boundary conditions,
both for the full systems and also within a smaller window within the system.
Our results appear to be fully compatible with a single pair of pure states
such as in the droplet/scaling picture. However, our results for whether or not
domain walls induced by changing boundary conditions are space filling or not
are also compatible with scenarios having many thermodynamic states, such as
the chaotic pairs picture and the replica symmetry breaking picture. The
differing results for spin overlaps in same and different boundary conditions
suggest that finite-size effects are very large for the system sizes currently
accessible in low-temperature simulations.
