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Assessing the role of static length scales behind glassy dynamics in polydisperse hard disks

J. Russo,Hajime Tanaka

Published 2015 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance The origin of dynamical slowing down toward glass transition is a fundamental unsolved problem in condensed matter physics. A crucial question is whether this slowing down has a structural origin. Recently, a method to detect hidden order within the fluid was proposed, based on the idea that freezing a fraction of the particles in a system causes a transition akin to glass transition. Here, we show that a glass former, polydisperse hard disks, has a strong increase of structural order, well correlated with slow dynamics, which goes undetected by the pinning method. This casts doubt on the order-agnostic qualities of the pinning length scale and keeps static length scales in the race for plausible explanations of the glass transition problem. The possible role of growing static order in the dynamical slowing down toward the glass transition has recently attracted considerable attention. On the basis of random first-order transition theory, a new method to measure the static correlation length of amorphous order, called “point-to-set” (PTS) length, has been proposed and used to show that the dynamic length grows much faster than the static length. Here, we study the nature of the PTS length, using a polydisperse hard-disk system, which is a model that is known to exhibit a growing hexatic order upon densification. We show that the PTS correlation length is decoupled from the steeper increase of the correlation length of hexatic order and dynamic heterogeneity, while closely mirroring the decay length of two-body density correlations. Our results thus provide a clear example that other forms of order can play an important role in the slowing down of the dynamics, casting a serious doubt on the order-agnostic nature of the PTS length and its relevance to slow dynamics, provided that a polydisperse hard-disk system is a typical glass former.

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