Active-to-absorbing-state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling

Abstract

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing-state phase transition, AAPT) in a model that by itself belongs to the directed percolation (DP) universality class, interacting with a spatiotemporally fluctuating environment having its own nontrivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic setup that, depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ, or EW equations), the system may show weak or strong dynamic scaling at the critical point of active-to-absorbing-state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.