Facilitated model for glasses

An analytical approach to the spin facilitated kinetic Ising model [Phys. Rev. Lett. 53, 1244 (1984); J. Chem. Phys. 84, 5822 (1985)] is proposed using a Fock space representation of the master equation. The cooperativity inherent in glassy materials is included by dynamical restrictions, which allows a change of local regions with different mobilities depending on the neighboring configurations. Applying a dynamical mean-field approximation, we get a non-Arrhenius relaxation behavior in the case of a simple activation dynamics for the kinetic coefficients. Whereas the short-time behavior is dominated by the conventional kinetic Ising model, the longtime limit is determined by the restrictions. Including an additional static interaction strength favoring a solidlike state, the relaxation time becomes drastically enlarged due to the partial freezing of the system. Related to this phenomenon the nucleation rate is strongly decreased, preventing the nucleation of droplets of the condensed phase. Analyzing the influence of spatial fluctuations, the perimeter of regions with extremely low mobility can be estimated in the long-time limit, resulting in a logarithmic behavior.