An Ising model for the thermal and dynamic properties of supercooled liquids and the glass transition

Abstract

We describe the behavior of an Ising model with orthogonal dynamics, where changes in energy and changes in alignment never occur during the same Monte Carlo (MC) step. This orthogonal Ising model (OIM) allows conservation of energy and conservation of momentum to proceed independently, on their own preferred time scales. MC simulations of the OIM mimic more than twenty distinctive characteristics that are commonly found above and below the glass temperature, Tg. Examples include a specific heat that has hysteresis around Tg, out-of-phase loss that exhibits primary and secondary peaks, super-Arrhenius T dependence for the alpha response time, and fragilities that increase with increasing system size (N). Mean-field theory for energy fluctuations in the OIM yields a novel expression for the super-Arrhenius divergence. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann (VFT) law squared, we call it the VFT2 law. A modified Stickel plot, which linearizes the VFT2 law, gives qualitatively consistent agreement with measurements of primary response (from the literature) on five glass-forming liquids. Such agreement with the OIM suggests that several basic features govern supercooled liquids. The freezing of a liquid into a glass involves an underlying 2nd-order transition that is broadened by finite-size effects. The VFT2 law comes from energy fluctuations that enhance the pathways through an entropy bottleneck, not activation over an energy barrier. Primary response times vary exponentially with inverse N, consistent with the distribution of relaxation times deduced from measurements. System sizes found via the T dependence of the primary response are similar to sizes of independently relaxing regions measured by nuclear magnetic resonance for simple-molecule glass-forming liquids. The OIM provides a broad foundation for more-detailed models of liquid-glass behavior.