On the Marginal Stability of Glassy Systems

In various glassy systems that are out of equilibrium, like spin glasses and granular packings, the dynamics appears to be critical: avalanches involving almost the whole system could happen. A recent conceptual breakthrough argues that such glassy systems sample the ensemble of marginal stable states, which inevitably results into critical dynamics. However, it is unclear how the marginal stability is dynamically guaranteed. We investigate this marginal stability assumption by studying specifically the critical athermal dynamics of the Sherrington-Kirkpatrick model. We discuss how a pseudo-gap in the density distribution of local fields characterizing the marginal stability arises dynamically.