Conserved directed percolation: exact quasistationary distribution of small systems and Monte Carlo simulations

Abstract

We study symmetric sleepy random walkers, a model exhibiting an absorbing-state phase transition in the conserved directed percolation (CDP) universality class. Unlike most examples of this class studied previously, this model possesses a continuously variable control parameter, facilitating analysis of critical properties. We study the model using two complementary approaches: analysis of the numerically exact quasistationary (QS) probability distribution on rings of up to 22 sites, and Monte Carlo simulation of systems of up to 32000 sites. The resulting estimates for critical exponents β, β/ν ⊥ , and z, and the moment ratio m 211 = ρ 2 / ρ 2 (ρ is the activity density), based on finite-size scaling at the critical point, are in agreement with previous results for the CDP universality class. We find, however, that the approach to the QS regime is characterized by a different value of the dynamic exponent z than found in the QS regime.

Continuously varying critical order-parameter fluctuations in a parity conserving absorbing-state transition with long-range diffusion

“…Finally, we reported the critical order parameter distribution showing that it evolves from a nearly Gaussian profile for short-range diusion to an exponential-like form when 5 2 → / α . The reported critical distributions are quite distinct from those previously reported to hold in other non-equilibrium phase transitions with short-ranged dynamical rules [43][44][45].…”

“…The universality of the critical relative order parameter fluctuations actually signals the underlying universal scaling form of the own critical order parameter distribution, a feature that has been widely explored in equilibrium second-order phase transitions [37][38][39][40][41][42]. The corresponding literature on the critical order parameter distribution in non-equilibrium transitions has also been recently explored [43][44][45]. However, while previous studies of branching and annihilating random walkers with anomalous diusion have focused on the continuous variation of critical exponents, a detailed investigation of the possible non-universality of the critical moment ratio and the critical order parameter distribution in this class of models are still missing.…”

Contact processes in crowded environments

“…This modification to an off-lattice version of the CLG model measures the same exponents at or near the absorbing-state transition [18]. Other lattice models containing local stochastic activation, many absorbing states, and an additional symmetry also exhibit CLG exponents [19,20]. A more recent periodically sheared colloidal experiment with elliptical particles exhibits similar exponents as well [21].…”

Activity, diffusion, and correlations in a two-dimensional conserved stochastic sandpile

“…In [35], a one-dimensional ARW model under strong bias (particle displacements in one direction only) was found to exhibit mean-field-like critical behavior, where the unbiased version studied in [36] exhibits CDP critical behavior. Although the effect of a weak bias on critical behavior has not been studied, we note that any such bias (f ≠ 0) breaks a fundamental symmetry of the model.…”