Influence of the Ground-State Topology on the Domain-Wall Energy in the Edwards-Anderson +/- J Spin Glass Model

F. Roma, S. Risau-Gusman, A. J. Ramirez-Pastor, F. Nieto, E. E. Vogel

Published 2006-07-23, updated 2006-12-21Version 2

We study the phase stability of the Edwards-Anderson spin-glass model by analyzing the domain-wall energy. For the bimodal 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.