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Abstract
We investigate the nature of the low-energy, large-scale excitations
in the three-dimensional Edwards-Anderson Ising spin glass with
Gaussian couplings and free boundary conditions, by studying the
response of the ground state to a coupling-dependent perturbation
introduced previously.
The ground states are determined exactly for system sizes up
to 12^3 spins using a branch and cut algorithm.
The data are consistent with a picture where the surface
of the excitations is not space-filling, such
as the droplet or the ``TNT'' picture. When allowing for large
finite size correctios, the data are also consistent with
a picture with space-filling surface,
such as replica symmetry breaking.
We compare the results with data for periodic boundary conditions
obtained with a genetic algorithm, and discuss the effects of different
boundary conditions on finite-size correction. Finally, we analyze the
performance of our branch and cut algorithm,
finding that it is correlated with the existence of large-scale,
low-energy excitations.
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