We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that for any finite periodic lattice and for mixing parameter $\lambda =1/2$, the system almost surely reaches the absorbing all-zero configuration in finitely many steps. In addition, Monte Carlo simulations indicate as well the presence of a zero-density stationary state in a finite interval around $\lambda =1/2$. Despite this absorbing behavior, both mean-field and block-approximation schemes predict a stationary state with nonzero density. This failure highlights a fundamental limitation of finite-block approximation in capturing the global dynamics of probabilistic cellular automata.

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• Dynamical phase transitions
• Cellular automata
• Mean-field & cluster methods