Critical behavior of nonequilibrium q-state systems

We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer $q>1$, and is defined on configurations of $q$-valued spins on regular lattices. The definitions of the models are very similar to the updating rules in Wolff's algorithm for the Potts model, but both classes break detailed balance, except for $q=2$ and $q=\infty$. In the first case both models reduce to the Ising model, while one of them reduces to percolation (more precisely, to the general epidemic process) for $q=\infty$. Locations of the critical point and critical exponents are estimated in 2 dimensions.