Whether or not there is growing static order accompanying the dynamical
heterogeneity and increasing relaxation times seen in glassy systems is a
matter of dispute. An obstacle to resolving this issue is that the order is
expected to be amorphous and so not amenable to simple order parameters. We use
mutual information to provide a general measurement of order that is sensitive
to multi-particle correlations. We apply this to two glass-forming systems (2D
binary mixtures of hard disks with different size ratios to give varying
amounts of hexatic order) and show that there is little growth of amorphous
order in the system without crystalline order. In both cases we measure the
dynamical length with a four-point correlation function and find that it
increases significantly faster than the static lengths in the system as density
is increased. We further show that we can recover the known scaling of the
dynamic correlation length in a kinetically constrained model, the 2-TLG.Comment: 10 pages, 12 Figure
