We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to non-zero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. <p> We...</p>

We show that predicting the HPP or FHP III lattice gas for finite time is equivalent to calculating the output of an arbitrary Boolean circuit, and is therefore P-complete: that is, it is just as hard as any other problem solvable by a serial computer in polynomial time. <p> It is widely believed...</p>

We introduce a simple spin model which shows glassy behavior at low temperatures, despite a Hamiltonian which is completely homogeneous and possesses no randomness; ergodicity breaking in this model is due entirely to the model's dynamics. We solve exactly for the model's equilibrium partition...