Disordered one-dimensional contact process

Theoretical and numerical analyses of the one-dimensional contact process with quenched disorder are presented. We derive scaling relations which differ from their counterparts in the pure model, and that are valid not only at the critical point but also away from it due to the presence of generic scale invariance. All the proposed scaling laws are verified in numerical simulations. In addition, we map the disordered contact process into a non-Markovian contact process by using the so called run time statistics, and write down the associated field theory. This turns out belong to the same universality class as the one derived by Janssen [Phys. Rev. E 55, 6253 (1997)] for the quenched system with a Gaussian distribution of impurities. Our findings reported herein support the lack of universality suggested by the field-theoretical analysis: generic power-law behaviors are obtained. We moreover show the absence of a characteristic time away from the critical point, and the absence of universality is put forward. The intermediate sublinear regime predicted by Bramsom, Durret, and Schnmann [Ann. Prob. 19, 960 (1991)] is also found.