An analytical approach to the Fredrickson-Andersen model with vacancies

The dynamics of the n-spin facilitated kinetic Ising model (Fredrickson-And ersen model) with mobile vacancies as a model for the glassy materials are studied analytically by means of the Pock-space representation of the maste r equation. The system is mapped onto a three state model characterizing mo bile, immobile and vacant cells. The characteristic cooperativity for glass forming systems are introduced by restrictions influencing the local dynam ics and subsequently the local mobility of different lattice cells. In a mo derate temperature regime the relaxation time versus the inverse temperatur e T-1 reveals two processes. Whereas the slow process can be identified wit h the conventional alpha-process of the supercooled liquid, the fast one or iginated by the additional empty sites is suggested to be the beta(JG)-proc ess due to Johari-Goldstein. The results are accordant with numerical simul ations and suggest that the modified n-spin facilitated kinetic Ising model is able to describe qualitatively the behaviour of a supercooled liquid ne ar the glass transition temperature T-g.