Abstract
We study the phase stability of the Edwards-Anderson spin glass
model by analyzing the domain-wall energy. For a bimodal $J$
distribution of bonds, a topological analysis of the ground state
allows us to separate the system into two regions: the backbone
and its environment. We find that the distributions of domain-wall
energies are very different in these two regions for the
three-dimensional (3D) case. Although the backbone turns out to
have a very high phase stability, the combined effect of these
excitations and correlations produces the low global stability
displayed by the system as a whole. On the other hand, in two
dimensions (2D) we find that the surface of the excitations avoids
the backbone. Our results confirm that a narrow connection exists
between the phase stability of the system and the internal
structure of the ground state. In addition, for both 3D and 2D we
are able to obtain the fractal dimension of the domain wall by
direct means.
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