On the absence of the glass transition in two dimensional hard disks

In this paper we study the glass transition in a model of identical hard spheres, focusing on the two dimensional case. In the mean-field limit the model exhibits an ideal glass transition of the same nature of that found in discontinuous spin glasses. Nevertheless, a systematic expansion around the mean-field solution seems to indicate that the glass transitions is smeared out in two dimensions, in agreement with some recent results. Our investigation could be generalized to higher spatial dimensions, providing a way to determine the lower critical dimensionality of the mean-field ideal glass picture.