Signature of the Ground-State Topology in the Low-Temperature Dynamics of Spin Glasses

We numerically address the issue of how the ground state topology is reflected in the finite temperature dynamics of the $\pm J$ Edwards-Anderson spin glass model. In this system a careful study of the ground state configurations allows to classify spins into two sets: solidary and non-solidary spins. We show that these sets quantitatively account for the dynamical heterogeneities found in the mean flipping time distribution at finite low temperatures. The results highlight the relevance of taking into account the ground state topology in the analysis of the finite temperature dynamics of spin glasses.