Does an ideal glass transition occur at finite temperature in 3D
In plain words
If one extrapolates the entropy of a cooling liquid, it seems to drop to that of the crystal at a finite temperature, the Kauzmann temperature, where an ideal glass would form. Whether this really happens, or the extrapolation fails, is unknown.
Precise statement
For 3D glass formers with short-range interactions in equilibrium, determine whether the configurational entropy $s_{c}(T)$ (total entropy minus the vibrational entropy of the inherent structures) vanishes at a finite Kauzmann temperature $T_{K} > 0$ with a thermodynamic singularity, or remains positive down to $T = 0$. An answer is a proof for a realistic model or finite-size-scaling evidence (configurational entropy, point-to-set length, overlap fluctuations) from equilibrium data below $T_{g}$ that discriminates the two cases.
What would settle it
Equilibrium simulations reaching temperatures where $s_c(T)$ and the point-to-set length either extrapolate to a finite-T singularity with finite-size scaling, or are shown to stay regular, in a $3\mathrm{D}$ model.
Status in the literature
Unverified note
Equilibrium simulations of $2\mathrm{D}$ glass formers since 2019 indicate a transition only at $T = 0$, and a 2025 numerical study revisited the $2\mathrm{D}$ case; the $3\mathrm{D}$ question remains open in 2026.