AN ANALYTICAL APPROACH TO THE FREDRICKSON–ANDERSEN MODEL WITH VACANCIES

Abstract

The dynamics of the n-spin facilitated kinetic Ising model (Fredrickson–Andersen model) with mobile vacancies as a model for the glassy materials are studied analytically by means of the Fock-space representation of the master equation. The system is mapped onto a three state model characterizing mobile, immobile and vacant cells. The characteristic cooperativity for glass forming systems are introduced by restrictions influencing the local dynamics and subsequently the local mobility of different lattice cells. In a moderate temperature regime the relaxation time versus the inverse temperature T-1 reveals two processes. Whereas the slow process can be identified with the conventional α-process of the supercooled liquid, the fast one originated by the additional empty sites is suggested to be the β JG -process due to Johari–Goldstein. The results are accordant with numerical simulations and suggest that the modified n-spin facilitated kinetic Ising model is able to describe qualitatively the behaviour of a supercooled liquid near the glass transition temperature T g .