We study the glassy transition for simple liquids in the hypernetted chain (HNC) approximation by means of an effective potential recently introduced. Integrating the HNC equations for hard spheres, we find a transition scenario analogous to that of the long range disordered systems with "one step replica symmetry breaking". Our result agree qualitatively with Monte Carlo simulations of three dimensional hard spheres.The HNC approximation is one of the most widely used approach to describe the density-density correlation function g(x) for liquids at equilibrium [1]. It consists in a self-consistent integral equation that can be derived by a partial resummation of the Meyer expansion, and corresponds to the variational equation for a suitable free-energy functional [2,3]. The simple HNC approach does not by itself allow to detect freezing [4]. The simple inspection of the pair correlation function certainly does not allow to do so, being qualitatively similar in the liquid and in the glass. Freezing, although present, can be hidden if one concentrates on simple equilibrium quantities [5].In has been recently stressed in [3] that the freezing transition can be detected combining the HNC approximation with the replica method by studying the correlation functions among different replicas of the same system in presence of a potential which couples them. At low temperature (or at high density) one finds a self-consistent solution where different replicas remains correlated also in the limit of zero coupling. This phenomenon correspond to freezing and it goes under the technical name of replica symmetry breaking.In this letter we pursue this idea of studying the glass transition in the HCN approximation. We are not concerned about the behavior in the glassy phase. Our aim it to use an effective potential recently introduced by two of us [6,7], to study the glass transition of HNC hard spheres in 3D. We compare the results with Monte Carlo simulations of real hard spheres. The conceptual advantage of this approach is that all the subtle points of the usual approach related to replica symmetry breaking are not needed in order to expose the transition.

Melting/freezing behavior of a fluid confined in porous glasses and MCM-41: Dielectric spectroscopy and molecular simulation By means of an effective potential associated with a constrained equilibrium measure and apt to study frozen systems, we investigate glassy freezing in simple liquids in the hypernetted chain ͑HNC͒ approximation. Unlike other classical approximations of liquid theory, freezing is naturally embedded in the HNC approximation. We give a detailed description of the freezing transition that is analogous to the one given in a large class of mean-field long range spin glass. We compare our findings with Monte Carlo simulations of the same system and conclude that many of the qualitative features of the transition are captured by the approximated theory.

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