The northeast model is a spin system on the two-dimensional integer lattice that evolves according to the following rule: whenever a site's southerly and westerly nearest neighbors have spin 1, it may reset its own spin by tossing a p-coin; at all other times, its spin remains frozen. It is proved that the northeast model has a phase transition at p c = 1 - βc, where βc is the critical parameter for oriented percolation. For p < p c, the trivial measure, δ0, that puts mass one on the

more »

... ation with all spins set at 0 is the unique ergodic, translation-invariant, stationary measure. For p ≥ p c, the product Bernoulli-p measure on configuration space is the unique nontrivial, ergodic, translation-invariant, stationary measure for the system, and it is mixing. For p > ⅔, it is shown that there is exponential decay of correlations.