Ground-state topology of the Edwards-Anderson +/-J spin glass model

TL;DR

This study investigates the ground-state backbone structure in the Edwards-Anderson spin glass model, revealing dimensional differences in percolation and a lower frustration in the backbone, with implications for understanding low-temperature phases.

Contribution

It provides a detailed numerical analysis of the backbone in 2D and 3D spin glasses, highlighting percolation behavior and frustration distribution, and proposes a generalized backbone concept for continuous bond distributions.

Findings

In 3D, the backbone percolates in the thermodynamic limit.

In 2D, the backbone likely does not percolate.

Frustration is significantly lower in the backbone than outside it.

Abstract

In the Edwards-Anderson model of spin glasses with a bimodal distribution of bonds, the degeneracy of the ground state allows one to define a structure called backbone, which can be characterized by the rigid lattice (RL), consisting of the bonds that retain their frustration (or lack of it) in all ground states. In this work we have performed a detailed numerical study of the properties of the RL, both in two-dimensional (2D) and three-dimensional (3D) lattices. Whereas in 3D we find strong evidence for percolation in the thermodynamic limit, in 2D our results indicate that the most probable scenario is that the RL does not percolate. On the other hand, both in 2D and 3D we find that frustration is very unevenly distributed. Frustration is much lower in the RL than in its complement. Using equilibrium simulations we observe that this property can be found even above the critical temperature. This leads us to propose that the RL should share many properties of ferromagnetic models, an idea that recently has also been proposed in other contexts. We also suggest a preliminary generalization of the definition of backbone for systems with continuous distributions of bonds, and we argue that the study of this structure could be useful for a better understanding of the low temperature phase of those frustrated models.