Critical behavior of a probabilistic cellular automaton describing a biological system

We study nonequilibrium phase transitions occurring in a probabilistic cellular automaton which describes one part of the immune system. In this model, each site can be occupied by three type of cells and the immune response under parasitic infections is described in terms of two parameters p and r. The local rules governing the evolution of this automaton possess “up–down” symmetry similar to Ising models. Performing Monte Carlo simulations on square and cubic lattices we verify that the model displays continuous kinetic phase transitions with spontaneous symmetry breaking. We present detailed simulations and analysis of the critical behavior. Our results indicate that the model belongs to the Ising universality class, supporting the “up–down” conjecture.