Critical droplets in metastable states of probabilistic cellular automata

摘要

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule that is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters beta and h that resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when beta is large enough and it is zero, and a unique phase when h is nonzero. When the system evolves, at small positive values of h, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored + phase inside the metastable - phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero "temperature" (beta-->infinity); as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions. [References: 29]