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

TL;DR

This study investigates how the ground-state topology influences domain-wall energies in the Edwards-Anderson spin glass model, revealing differences between 2D and 3D cases and linking internal structure to phase stability.

Contribution

It provides a topological analysis of ground states and connects the internal structure to phase stability, including fractal dimension measurements of domain walls.

Findings

High phase stability of the backbone in 3D

Different domain-wall energy distributions in backbone and environment

Fractal dimension of domain walls measured in 2D and 3D

Abstract

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.