Robustness of directed percolation under relaxation of prerequisites: role of quenched disorder and memory

Directed percolation (DP) is the most widely observed transition to the absorbing state in the nonequilibrium systems. For all continuous transitions with positive one-component order parameter, short-range processes in space and time, and without additional symmetries or quenched disorder, DP is the expected universality class. We study the robustness of the DP universality class under the relaxation of these conditions. (a) We consider two types of particles, A and B such that A sites recover in one time-step with probability 1 - p , while type B definitely recovers in τ time-steps. (b) A fraction of sites are coupled to nearest neighbors and the rest are coupled to the next-nearest neighbor. (c) The sites infected in previous t m time-steps are infected with lower probability p 1 and the rest are infected with probability p . (d) We examine the effect of global external forcing on the contact process. (e) We study the relevance of quenched disorder in coupled map lattice. (f) We study connections to a common manifold in a 2D contact process. These infinite long-range connections lead to the DP universality class in 1D. In all these cases except power-law forcing with a small decay exponent and large delay in model (a), the order-parameter decay exponent stays in the DP class. Thus, the DP universality class is robust under the relaxation of many of its prerequisites. Graphic abstract