  The small wavenumber $k$ behavior of the structure factor $S(k)$ of
overcompressed amorphous hard-sphere configurations was previously studied for
a wide range of densities up to the maximally random jammed state, which can be
viewed as a prototypical glassy state [A. Hopkins, F. H. Stillinger and S.
Torquato, Phys. Rev. E, 86, 021505 (2012)]. It was found that a precursor to
the glassy jammed state was evident long before the jamming density was reached
as measured by a growing nonequilibrium length scale extracted from the volume
integral of the direct correlation function $c(r)$, which becomes long-ranged
as the critical jammed state is reached. The present study extends that work by
investigating via computer simulations two different atomic models: the
single-component Z2 Dzugutov potential in three dimensions and the
binary-mixture Kob-Andersen potential in two dimensions. Consistent with the
aforementioned hard-sphere study, we demonstrate that for both models a
signature of the glass transition is apparent well before the transition
temperature is reached as measured by the length scale determined from from the
volume integral of the direct correlation function in the single-component case
and a generalized direct correlation function in the binary-mixture case. The
latter quantity is obtained from a generalized Orstein-Zernike integral
equation for a certain decoration of the atomic point configuration. We also
show that these growing length scales, which are a consequence of the
long-range nature of the direct correlation functions, are intrinsically
nonequilibrium in nature as determined by an index $X$ that is a measure of
deviation from thermal equilibrium. It is also demonstrated that this
nonequilibrium index, which increases upon supercooling, is correlated with a
characteristic relaxation time scale.
