Critical behavior of the one-dimensional diffusive pair contact process

Abstract

The phase transition of the one-dimensional, diffusive pair contact process (PCPD) is investigated by N cluster mean-field approximations and high precision simulations. The N = 3, 4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with β2 = 2 mean-field order parameter exponent of the pair density. This contradicts with former N = 2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L = 10 5 lattices give estimates for the order parameter exponents of the particles for 0.05 ≤ D ≤ 0.7. These data can support former two distinct class findings. However the gap between low and high D exponents is narrower than estimated previously and the possibility for interpreting numerical data as a single class behavior with exponents α = 0.21(1), β = 0.41(1) assuming logarithmic corrections is shown. Finite size scaling and cluster simulation results are also presented.

The non-equilibrium phase transition of the pair-contact process with diffusion

“…This result strongly suggests that there is only one universality class along the critical line [52]. This finding is in agreement with simulational results, see section 4.…”

“…Consider first the PCP where It is then natural to extend this study to the whole phase diagram. This was done in [52], including the quartet approximation (N = 4). As can be seen in figure 2 the kink in p c (D) observed in the pair approximation is absent for larger clusters.…”

“…This paper was followed by a long series of numerical and analytical studies [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] and released the still ongoing debate concerning the asymptotic critical behaviour of the PCPD at the transition. Until now a surprising variety of possible scenarios has been proposed, the main viewpoints being that the active-absorbing phase transition in the PCPD -should represent a novel universality class with a unique set of critical exponents [38,44,48,51], -may represent two different universality classes depending on the diffusion rate [39,52] and/or the number of space dimensions [53], -can be interpreted as a cyclically coupled DP and annihilation process [40], -could be regarded as a marginally perturbed DP process with continuously varying critical exponents [47], -may have exponents depending continuously on the diffusion constant D [49,56], -may cross over to DP after very long time [50,54], and -is perhaps related to the problem of non-equilibrium wetting in 1+1 dimensions [55].…”

Critical decay exponent of the pair contact process with diffusion

“…For example, the reported critical point ≈0.133 53 of the case with D = 0.5 in Ref. [27] is consistent with that in Ref. [14] which is ≈ 0.133 519.…”

Critical behavior of nonequilibrium continuous phase transition inA+BCcatalytic reaction system

“…Dickman has noted that the continuous phase transition in the contact process (CP) model including the diffusion still belongs to the DP universality class [22]. However, a study of the pair contact process with diffusion (PCPD) or annihilation-fission (AF) process 2A → ,2A → 3A suggests that the diffusion of the particles should introduce a new kind of critical behavior [23][24][25][26][27][28][29][30][31][32]. This model without diffusion was first investigated by Jensen, and its critical behavior of the continuous transition with infinitely many absorbing states belongs to the DP class [13].…”