Study of continuous phase transition with Toom cellular automata

The heuristic proof, based on computer simulation investigations, is presented that though stationary Toom cellular automata exhibit many features which are characteristic for an equilibrium system (e.g. rapid change in the order parameter, when noise is fine tuned, or slow decay of the two point correlation function), the stationary state is not Gibbsian. It means that it is impossible to define energy on the microscopic level in such a way that the dynamic system becomes representative of some equilibrium lattice model. Moreover, properties on the coarse-grained level: fluctuations, seem to be distinct from the corresponding ones of the Ising model.