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We describe the behavior of an Ising model with orthogonal dynamics, wherechanges in energy and changes in alignment never occur during the same MonteCarlo (MC) step. This orthogonal Ising model (OIM) allows conservation ofenergy and conservation of momentum to proceed independently, on their ownpreferred time scales. MC simulations of the OIM mimic more than twentydistinctive characteristics that are commonly found above and below the glasstemperature, Tg. Examples include a specific heat that has hysteresis aroundTg, out-of-phase loss that exhibits primary and secondary peaks,super-Arrhenius T dependence for the alpha response time, and fragilities thatincrease with increasing system size (N). Mean-field theory for energyfluctuations in the OIM yields a novel expression for the super-Arrheniusdivergence. Because this divergence is reminiscent of the Vogel-Fulcher-Tammann(VFT) law squared, we call it the VFT2 law. A modified Stickel plot, whichlinearizes the VFT2 law, gives qualitatively consistent agreement withmeasurements of primary response (from the literature) on five glass-formingliquids. Such agreement with the OIM suggests that several basic featuresgovern supercooled liquids. The freezing of a liquid into a glass involves anunderlying 2nd-order transition that is broadened by finite-size effects. TheVFT2 law comes from energy fluctuations that enhance the pathways through anentropy bottleneck, not activation over an energy barrier. Primary responsetimes vary exponentially with inverse N, consistent with the distribution ofrelaxation times deduced from measurements. System sizes found via the Tdependence of the primary response are similar to sizes of independentlyrelaxing regions measured by nuclear magnetic resonance for simple-moleculeglass-forming liquids. The OIM provides a broad foundation for more-detailedmodels of liquid-glass behavior.

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