Ising Model of the Glassy Correlation Length

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.