A general approach to systems with randomly pinned particles: unfolding and clarifying the Random Pinning Glass Transition

Pinning a fraction of particles from an equilibrium configuration in supercooled liquids has been recently proposed as a way to induce a new kind of glass transition, the Random Pinning Glass Transition (RPGT). The RPGT has been predicted to share some features of standard thermodynamic glass transitions and usual first order ones. Thanks to its special nature, the approach and the study of the RPGT appears to be a fairly reachable task compared to the daunting problem of inspecting standard glass transitions. In this Letter we generalize the pinning particle procedure. We study a mean-field system where the pinned configuration is extracted from the equilibrium distribution at temperature $T'$ and the thermodynamics of the non pinned particles is observed at a lower temperature $T$. A more complicated physics emerges from this generalization eventually clarifying the origin and the peculiar characteristics of the RPGT.