Investigating amorphous order in stable glasses by random pinning

We use a random pinning procedure to investigate stable glassy states associated with large deviations of the activity in a model glass-former. We pin particles both from active (equilibrium) configurations and from stable (inactive) glassy states. By comparing the distribution of the overlap between states that share pinned particles, we infer that the inactive states are characterised by a structural length scale that is comparable with the system size. This is a manifestation of amorphous order in these glassy states, which helps to explain their stability.