Violation of scaling in the contact process with quenched disorder

We study the two-dimensional contact process (CP) with quenched disorder (DCP), and determine the static critical exponents beta and nu(perpendicular to). The dynamic behavior is incompatible with scaling, as applied to models (such as the pure CP) that have a continuous phase transition to an absorbing state. We find that the survival probability (starting with all sites occupied), 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 nu(parallel to), 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 (1996)] is further evidence of violation of scaling. A simple argument based on percolation cluster statistics yields a similar logarithmic evolution. [S1063-651X(98)02702-0].