A modified facilitated kinetic Ising model for supercooled liquids

A modification is considered of the well-known Fredrickson-Andersen facilit ated kinetic Ising model for studying the glass transition in supercooled l iquids. In this modification, which we call the cluster facilitated kinetic Ising model (CluFKI) model, the Rip of a spin between the liquid-like regi ons represented by A or up states and the solid-like regions represented by B or down states can occur (i.e. is facilitated) only if in the cluster co ntaining the spin and those adjacent to it there are at least n spins in th e A state. As a result, the transition from a solid-like to a liquid-like r egion requires more free volume than the reverse transition, which is physi cally very reasonable. Computer calculations for the n = 1 CluFKI model, as well as a qualitative analysis, show that as the temperature T of the syst em decreases, and so the parameter x = E/T increases, the fraction fa of sp ins in state A when the system is in a metastable steady state decreases un til it reaches zero for a critical value x,. Correspondingly, the mean rela xation time (tau) of the system's memory function increases rapidly, and (t au) --> infinity as x --> x(c). This behaviour is similar to that for the o r-relaxation in supercooled liquids as the glass transition temperature is approached.