1207.6349 (J. S. Langer)

Ising Model of the Glassy Correlation Length    [PDF]

J. S. Langer

Recent numerical simulations indicate that several different equilibrium glass transitions are characterized by a diverging correlation length, and that this divergence is described by a non-mean-field, Ising-like, critical exponent. I argue here that a minimal model of a polydisperse system, in which the particles interact only via hard-core repulsions, 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.

View original: http://arxiv.org/abs/1207.6349