Competitive nucleation in reversible probabilistic cellular automata

The problem of competitive nucleation in the framework of probabilistic cellular automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self-interaction is discussed. An intermediate metastable phase, made of two flip-flopping chessboard configurations, shows up depending on the ratio between the magnetic field and the self-interaction. A behavior similar to the one of the stochastic Blume-Capel model with Glauber dynamics is found.

Figure 1

The time unit is the time step of the chain. Solid lines (from the left-hand side to the right-hand side) represent the magnetization of the runs $(\kappa ,\beta )=(0.15,0.55),(0.4,0.5),(0,025,0.7)$. Dashed lines represent the absolute value of the staggered magnetization; the non-null curve is found for $(\kappa ,\beta )=(0.025,0.7)$.