We study critical spreading dynamics in the two-dimensional contact process (CP) with quenched disorder in the form of random dilution. In the pure model, spreading from a single particle at the critical point λ c is characterized by the critical exponents of directed percolation: in 2+1 dimensions, δ = 0.46, η = 0.214, and z = 1.13. Disorder causes a dramatic change in the critical exponents, to δ ≃ 0.60, η ≃ −0.42, and z ≃ 0.24. These exponents govern spreading following a long crossover period. The usual hyperscaling relation, 4δ + 2η = dz, is violated. 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.

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We study the two-dimensional contact process ͑CP͒ with quenched disorder ͑DCP͒, and determine the static critical exponents ␤ and Ќ . The dynamic behavior is incompatible with scaling, as applied to models ͑such as the pure CP͒ that have a continuous phase transition to an absorbing state. We find that the survival probability ͑starting with all sites occupied͒, for a finite-size system at the critical point, decays according to a power law, as does the off-critical density autocorrelation function. Thus the critical exponent ͉͉ , which governs the relaxation time, is undefined, since the characteristic relaxation time is itself undefined. The logarithmic time dependence found in recent simulations of the critical DCP ͓A. G. Moreira and R. Dickman, Phys. Rev. E 54, R3090 ͑1996͔͒ is further evidence of violation of scaling. A simple argument based on percolation cluster statistics yields a similar logarithmic evolution.

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