Abstract
A simple spatially two-dimensional stochastic cellular automaton with asymmetric coupling and synchronous updating according to Glauber rates is considered. While detailed balance is violated it is still possible to compute analytically the stationary probability distribution by elementary means. The stationary distribution can be written as a canonical equilibrium distribution of a spin system on a triangular lattice with nearest neighbour coupling. Thus, the cellular automaton shows a nonequilibrium phase transition with Ising critical behaviour.
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