  The possible role of growing static order in the dynamical slowing down
towards the glass transition has recently attracted considerable attention. On
the basis of random first-order transition (RFOT) 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, 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.
