Adam Nahum: The damage-spreading phase transition: an infinite hierarchy of renormalization-group fixed points

Deterministic classical cellular automata can be in two phases, depending on how irreversible the dynamical rules are. In the strongly irreversible phase, trajectories with different initial conditions coalesce quickly. In the weakly irreversible phase, trajectories with different initial conditions can remain different for a long time (exponential in system volume). The simplest setting is a random classical circuit --- e.g. a random sequence of Boolean operations on bits --- where it is possible to tune to a continuous transition between the two phases. This phase transition has long been known to be related to directed percolation. We argue that the transition is, however, richer than directed percolation, and is interesting from the point of view of the RG. There is an infinite hierarchy of sectors of observables, with directed percolation describing the first level of the hierarchy. The higher sectors are related to absorbing state transitions for multiple species of particles.