Geometrical Frustration and Static Correlations in a Simple Glass Former

We study the geometrical frustration scenario of glass formation for simple hard-sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing down of relaxation, because of the strong frustration characterizing these systems. The possibility of a growing static length is furthermore found to be physically irrelevant in the regime that is accessible to computer simulations.

Figure 1

Evolution of $\overline{q}$ and (left inset) of the probability distribution $p(q)$ with density. The statistical honeycomb limit is given for reference. (right inset) Network of $q=6$ spindles (rods) at $\varphi =0.58$.

Figure 2

Long-time limit of the overlap. (inset) Time $t$ evolution of the overlap for $c_{\mathrm{pin}}=0.11$, 0.45, 0.68, 0.74, and 0.79, from left to right, in $(\beta m{\sigma }^2{)}^{-1/2}$ units with mass $m$, the larger particle $\sigma$ and inverse temperature $\beta$ set to unity.

Figure 3

Various static lengths rescaled to unity at $\varphi =0.40$ (${\xi }_0$) together with the lower bound from Eq. (2) ${\xi }_{\mathrm{bound}}$ and the dynamic length [17]. (inset) Measures of dynamical slowdown. Lines are guide for the eyes.