Backbone structure of the Edwards-Anderson spin-glass model

TL;DR

This paper investigates the ground-state heterogeneities of the Edwards-Anderson spin-glass model, introducing a generalized backbone concept that applies to both bimodal and Gaussian bond distributions, and explores its impact on finite-temperature properties.

Contribution

It generalizes the backbone definition to continuous bond distributions and analyzes the topological structure of the backbone across different lattice dimensions.

Findings

Backbone structure is similar for discrete and continuous bonds.

Heterogeneities influence equilibrium properties at finite temperature.

Backbone may be relevant for understanding spin-glass phenomena.

Abstract

We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.