  We show in numerical simulations that a system of two coupled replicas of a
binary mixture of hard spheres undergoes a phase transition in equilibrium at a
density slightly smaller than the glass transition density for an unreplicated
system. This result is in agreement with the theories that predict that such a
transition is a precursor of the standard ideal glass transition. The critical
properties are compatible with those of an Ising system. The relations of this
approach to the conventional approach based on configurational entropy are
briefly discussed.
