Two competitive contact processes with local interactions

We present a simple lattice model that consists of two competitive contact processes with local interactions on a one-dimensional lattice. The sites of the lattice can be empty or occupied by particles of type A or type B. The time evolution of the densities is governed by a master equation, whose transition among the states depends essentially on the spreading and annihilation rates of both particles. This is a competitive model where the stationary states are determined as a function of the spreading and annihilation rates. We employ mean-field approximations, at the level of one and two sites, and we obtain a phase diagram that shows four well distinguished phases, including a mixed one in which both particles coexist. Monte Carlo simulations show that this mixed phase no longer exists in the limit of large one-dimensional lattices. However, simulations of the model in two dimensions show that the mixed phase does not disappear as in the one-dimensional case. We also calculate some static critical exponents of the one-dimensional version of the model and we have shown that they belong to the directed percolation universality class. (paper)