VIOLATION OF SCALING IN THE CONTACT PROCESS WITH QUENCHED DISORDER

We study the two-dimensional contact process (CP) with quenched disord er (DCP), and determine the static critical exponents beta and nu(perp endicular to). The dynamic behavior is incompatible with scaling, as a pplied to models (such as the pure CP) that have a continuous phase tr ansition to an absorbing state. We find that the survival probability (starting with all sites occupied), for a finite-size system at the cr itical point, decays according to a power law, as does the off-critica l density autocorrelation function. Thus the critical exponent nu(para llel to), which governs the relaxation time, is undefined, since the c haracteristic relaxation time is itself undefined. The logarithmic tim e dependence found in recent simulations of the critical DCP [A. G. Mo reira and R. Dickman, Phys. Rev. E 54, R3090 (1996)] is further eviden ce of violation of scaling. A simple argument based on percolation clu ster statistics yields a similar logarithmic evolution. [S1063-651X(98 )02702-0].