On the critical behavior of the specific heat in glass-formers

We show numeric evidence that, at low enough temperatures, the potential energy density of a glass-forming liquid fluctuates over length scales much larger than the interaction range. We focus on the behavior of translationally invariant quantities. The growing correlation length is unveiled by studying the Finite Size effects. In the thermodynamic limit, the specific heat and the relaxation time diverge as a power law. Both features point towards the existence of a critical point in the metastable supercooled liquid phase.