Griffiths-like phase in the three-dimensional $\pm J$ Edwards-Anderson spin-glass model

TL;DR

This study identifies a Griffiths-like phase in the three-dimensional $ ext{±}J$ Edwards-Anderson spin-glass model using ground state topology and damage spreading, revealing finite ferromagnetic clusters influencing phase behavior.

Contribution

It demonstrates the presence of a Griffiths-like phase in the 3D $ ext{±}J$ Edwards-Anderson model and links it to finite ferromagnetic clusters identified through damage spreading.

Findings

Damage spreads above the glass transition temperature $T_g$ with spin-flipping dynamics.

Finite ferromagnetic clusters cause damage spreading in the Griffiths-like phase.

The damage critical temperature $T_d$ is comparable to the ferromagnetic Ising model's critical temperature $T_c$.

Abstract

Using information of the ground state topology and the damage spreading technique we show a Griffiths-like phase is present in the three-dimensional $\pm J$ Edwards-Anderson spin glass model. With spin-flipping dynamics damage spreads for temperatures larger than $T_{\mathrm{g}}$, the glass transition temperature. With spin-orienting dynamics and for temperatures in $T_{\mathrm{g}} < T < T_{\mathrm{d}}$, damage spreads over a finite region of the system, composed of finite clusters of ferromagnetic character. $T_{\mathrm{d}}$ is the spin-orienting damage critical temperature, which is of the same order as the critical temperature of the ferromagnetic Ising model, $T_{\mathrm{c}}$. The present results allow us to identify the clusters which originate the Griffiths-like phase in the present model.