Lennard-Jones binary mixture: a thermodynamical approach to glass transition

We study the liquid-glass transition of the Lennard-Jones binary mixture introduced by Kob and Andersen from a thermodynamic point of view. By means of the replica approach, translating the problem in the study of a molecular liquid, we study the phase transition due to the entropy crisis and we find that the Kauzmann's temperature $\tk$ is $\sim 0.32$. At the end we compare analytical predictions with numerical results.