Damage-spreading and out-of-equilibrium dynamics in the low-temperature regime of the two-dimensional ± J Edwards–Anderson model

Abstract

We present results showing the correlation between the out-of-equilibriumdynamics and the equilibrium damage-spreading process in the two-dimensional ± J Edwards–Anderson model at low temperatures. A key ingredient in our analysis is theprojection of finite temperature spin configurations onto the ground state topology ofthe system. In particular, through numerical simulations we correlate groundstate information with the out-of-equilibrium dynamics. We also analyse how thepropagation of a small perturbation in equilibrated systems is related to the groundstate topology. This damage-spreading study unveils the presence of rigid clustersof spins. We claim that these clusters give rise to the slow out-of-equilibriumdynamics observed in the temperature range between the glass temperatureTg = 0 of thetwo-dimensional ± J Edwards–Anderson model and the critical temperatureTc of the pure ferromagnetic Ising model.