  Recent numerical simulations indicate that several different equilibrium
glass transitions may be characterized by diverging correlation lengths, and
that these divergences are described by a non-mean-field, Ising-like, critical
exponent. I argue here that a minimal model of polydisperse, hard-core
particles can be reformulated in terms of Ising spins. The two spin states
correspond, at high pressure, to two compact, local topologies -- "solidlike"
and "liquidlike" -- whose average volumes per particle are nearly identical for
strongly frustrated, glass forming systems. The critical correlations in this
system imply a Vogel-Fulcher-Tamann formula for the structural relaxation time.
The theory also predicts, however, that realistic glass-forming systems
generally are not exactly critical and, therefore, do not exhibit ideal glass
transitions at low temperatures or high pressures.
