Do Binary Hard Disks Exhibit an Ideal Glass Transition?

TL;DR

This paper shows that binary hard-disk mixtures do not have an ideal glass transition, as an exponential number of jammed packings exist across a range of densities, indicating non-zero configurational entropy.

Contribution

It explicitly constructs numerous jammed packings in binary hard disks, challenging the notion of an ideal glass transition and the associated zero configurational entropy.

Findings

No zero configurational entropy at the supposed ideal glass transition.

Existence of exponentially many jammed packings across density spectrum.

Challenges the theoretical basis for an ideal amorphous glass state.

Abstract

We demonstrate that there is no ideal glass transition in a binary hard-disk mixture by explicitly constructing an exponential number of jammed packings with densities spanning the spectrum from the accepted ``amorphous'' glassy state to the phase-separated crystal. Thus the configurational entropy cannot be zero for an ideal amorphous glass, presumed distinct from the crystal in numerous theoretical and numerical estimates in the literature. This objection parallels our previous critique of the idea that there is a most-dense random (close) packing for hard spheres [Torquato et al, Phys. Rev. Lett., 84, 2064 (2000)].