STATICS AND DYNAMICS OF THE 2-SPIN-FACILITATED KINETIC ISING-MODEL

The two-spin-facilitated kinetic Ising model, or Fredrickson-Andersen model, in two dimensions is investigated, where down-spins are energetically favored over up-spins due to a suitably oriented magnetic field and the only interaction between spins is a dynamic constraint which allows any spin to flip only if it has at least two nearest up-spin neighbors. From Monte Carlo simulations it is known that the model exhibits glasslike behavior where the autocorrelation time of a spin as a function of temperature is well described by the Adam-Gibbs expression. Due to the dynamic constraint, the state space is divided into nonconnected partitions the most important of which is the high temperature partition which includes the all-spins-up state. A proof given earlier by Fredrickson and Andersen is completed, which states that for infinitly large lattices and for a temperature larger than zero, the probability that a randomly picked state is part of the high temperature partition approaches unity. It is also shown that the system is ergodic, i.e, that no glass transition may occur at a temperature larger than zero. These results hold also for the model in higher dimensions than two and for the three-spin-facilitated kinetic Ising model in three dimensions. It is suggested that the model equilibrates by cooperative diffusion of a critical droplet of up-spins.