Critical dynamics of the contact process with quenched disorder

We study critical spreading in Monte Carlo simulations of the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the purl model, spreading from a single particle at the critical point lambda(c) follows power laws with the critical exponents of directed percolation. With disorder, critical spreading is logarithmic not power law. Below lambda(c) there is a Griffiths phase in which the time dependence is governed by nonuniversal power laws. The effects of disorder are also apparent above lambda(c), in the active phase, where the relaxation of the survival probability is algebraic, rather than exponential, as in the pure model. Our results support the conjecture by Bramson, Durrett, and Schonmann [Ann. Prob. 19, 960 (1991)], that in two or more dimensions the disordered CP has only a single phase transition.