Mean-field glass transition in a model liquid

We investigate the liquid-glass phase transition in a system of pointlike particles interacting via a finite-range attractive potential in D -dimensional space. The phase transition is driven by an “entropy crisis” where the available phase space volume collapses dramatically at the transition. We describe the general strategy underlying the first-principles replica calculation for this type of transition; its application to our model system then allows for an analytic description of the liquid-glass phase transition within a mean-field approximation, provided the parameters are chosen suitably. We find a transition exhibiting all the features associated with an entropy crisis, including the characteristic finite jump of the order parameter at the transition while the free energy and its first derivative remain continuous.