  A theoretical description of the low-temperature phase of short-range spin
glasses has remained elusive for decades. In particular, it is unclear if
theories that assert a single pair of pure states, or theories that are based
infinitely many pure states-such as replica symmetry breaking-best describe
realistic short-range systems. To resolve this controversy, the
three-dimensional Edwards-Anderson Ising spin glass in thermal boundary
conditions is studied numerically using population annealing Monte Carlo. In
thermal boundary conditions all eight combinations of periodic vs antiperiodic
boundary conditions in the three spatial directions appear in the ensemble with
their respective Boltzmann weights, thus minimizing finite-size corrections due
to domain walls. From the relative weighting of the eight boundary conditions
for each disorder instance a sample stiffness is defined, and its typical value
is shown to grow with system size according to a stiffness exponent. An
extrapolation to the large-system-size limit is in agreement with a description
that supports the droplet picture and other theories that assert a single pair
of pure states. The results are, however, incompatible with the mean-field
replica symmetry breaking picture, thus highlighting the need to go beyond
mean-field descriptions to accurately describe short-range spin-glass systems.
