  Probabilistic cellular automata describe the dynamics of classical spin
models, which, for sufficiently small temperature $T$, can serve as classical
memory capable of storing information even in the presence of nonzero external
magnetic field $h$. In this article, we study a recently-introduced
probabilistic cellular automaton, the sweep rule, and map out a region of two
coexisting stable phases in the $(T,h)$ plane. We also find that the sweep rule
belongs to the weak two-dimensional Ising universality class. Our work is a
step towards understanding how simple geometrically-local error-correction
strategies can protect information encoded into complex noisy systems, such as
topological quantum error-correcting codes.
