Domain growth within the backbone of the three-dimensional $\pm J$ Edwards-Anderson spin glass

TL;DR

This paper demonstrates the presence of ferromagnetic-like domain growth within the backbone of the 3D $ ext{±}J$ Edwards-Anderson spin glass, revealing spatial heterogeneities linked to out-of-equilibrium dynamics.

Contribution

It introduces a method to detect domain walls in the EA spin glass, showing a domain growth process within its backbone, extending insights from the ferromagnetic Ising model.

Findings

Correlation functions reveal spatial heterogeneities.

Mean flipping time distribution indicates dynamical heterogeneities.

Domain growth process identified within the backbone of the EA model.

Abstract

The goal of this work is to show that a ferromagnetic-like domain growth process takes place within the backbone of the three-dimensional $\pm J$ Edwards-Anderson (EA) spin glass model. To sustain this affirmation we study the heterogeneities displayed in the out-of-equilibrium dynamics of the model. We show that both correlation function and mean flipping time distribution present features that have a direct relation with spatial heterogeneities, and that they can be characterized by the backbone structure. In order to gain intuition we analyze the pure ferromagnetic Ising model, where we show the presence of dynamical heterogeneities in the mean flipping time distribution that are directly associated to ferromagnetic growing domains. We extend a method devised to detect domain walls in the Ising model to carry out a similar analysis in the three-dimensional EA spin glass model. This allows us to show that there exists a domain growth process within the backbone of this model.