We present a brief overview of two key aspects of the structural glass transition (GT). The first part analyzes the structural slowing down in supercooled liquids, culminating in the kinetic GT predicted by mode-coupling theory (MCT); the theoretical predictions are confronted with the results of Molecular Dynamics simulations. The second part of the review examines the still controversial “random first order transition” (RFOT) from a quenched liquid to an “ideal glass” expected to occur at much lower temperatures,
where equilibration times diverge, making the RFOT inaccessible to experiment and simulation. A “pedestrian” but robust version of the replica formalism (involving two weakly coupled replicae) is combined with integral equations for the pair structure of such a symmetric binary system, and leads to the prediction of a thermodynamic, weakly first-order RFOT both for the “soft sphere” and Lennard-Jones models, via qualitatively identical scenarios.
