Restricted exclusion processes without particle conservation flows to directed percolation

Abstract

Absorbing phase transition in restricted exclusion processes are characterized by simple integer exponents. We show that this critical behaviour flows to the directed percolation (DP) universality class when particle conservation is broken suitably. The same transition, when studied using the average density as the controlling parameter, yields critical exponents quite different from DP; we argue that these exponents are actually related to DP by a scaling factor 1/βDP . These conclusions also apply to conserved lattice gas in one dimension.

Absorbing phase transition in energy exchange models

“…Once again, we find thatβ ≃ β DP . The other exponents like z and β/ν ⊥ for density are also found to be consistent with the corresponding DP values (data not shown here non-order parameter e − e c similar to some other models with infinitely many absorbing configurations [23,24].…”

Active-to-absorbing-state phase transition in an evolving population with mutation

“…This noise would then have survived in the absorbing state. We neglect this noise for simplicity, which is akin to assume a "low temperature limit" for species B. Interestingly, in the absence of an additive conserved noise in (7), ρ = 0, φ = 0 is also an absorbing state. We ignore this and focus on the absorbing state ρ = 0, φ = φ 0 = const.…”

“…Simplest models that exhibit AAPT often belong to the well-known directed percolation (DP) universality class. Some popular examples of systems showing DP universal scaling behavior [6,7] are the epidemic process with recovery or the Gribov process [8] and the predator prey cellular automation models [9][10][11][12]. In predator prey models for example [13,14], the growth (birth) and decay (death) of particles or species competes and thus there may be a finite density of the species in the steady state ("active state") or extinction of the species ("inactive/absorbing state").…”