A cluster facilitated kinetic Ising model for supercooled liquids

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Abstract
A fundamental modification is considered of the well-known Fredrickson-Andersen (FA) n-spin facilitated kinetic Ising model for studying the glass transition in supercooled liquids, in which the up spins correspond to a liquid-like state A and the down states to a solid-like state B. In our general model, which we call the n-spin cluster facilitated kinetic Ising model, a spin can flip from one state to the other (i.e. is facilitated) only if in the cluster containing the spin and those adjacent to it there are at least n up spins. Thus, in contrast to the FA model, it is easier for an up spin to flip than for one in the down state, which is the physically reasonable motivation for considering this class of models and leads to very different properties. In this communication, we consider the simplest case, namely n = 1, for which both a qualitative analysis and computer simulations show that as the temperature of the system decreases, the fraction fA of spins in state A when the system is in a metastable steady state decreases until it reaches zero at a critical temperature Tc, and the mean relaxation time of the system's memory function increases rapidly as Tc is approached.