Influence of the ground-state topology on domain-wall energy in the Edwards-Anderson ±J spin glass model

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.