Static point-to-set correlations in glass-forming liquids

We analyze static point-to-set correlations in glass-forming liquids. The generic idea is to freeze the position of a set of particles in an equilibrium configuration and to perform sampling in the presence of this additional constraint. Qualitatively different geometries for the confining set of particles are considered and a detailed comparison of resulting static and dynamic correlation functions is performed. Our results reveal the existence of static spatial correlations not detected by conventional two-body correlators, which appear to be decoupled from, and shorter-ranged than, dynamical length scales characterizing dynamic heterogeneity. We find that the dynamics slows down dramatically under confinement, which suggests new ways to investigate the glass transition. Our results indicate that the geometry in which particles are randomly pinned is the best candidate to study static correlations.

Figure 1

Four qualitatively different geometries to investigate point-to-set correlations in glass-forming liquids.

Figure 2

Time dependence of the overlaps $Q\left(t\right)$ (full lines) and $Q_{\mathrm{self}}\left(t\right)$ (dashed lines) for $T=8.0$. The panels correspond to the four geometries of Fig. 1. In (b) we have also included the results of fits with a stretched exponential to the $Q\left(t\right)$ data for $\Delta =2.25$ and $\Delta =3.25$ (dashed-dotted lines).

Figure 3

Time dependence of the overlap $Q\left(t\right)-Q_{\mathrm{rand}}$ (symbols) and the stretched exponential fits (lines) for the sandwich geometry and different values of $\Delta$.

Figure 4

(a) Dependence of the overlap $Q_{\infty }$ on the confining length for all geometries at $T=8$ (symbols) fitted with an exponential decay at long distances (straight lines). (b) Relaxation time of the self-overlap normalized by its bulk value.