Phase transitions of the binary production2A→3A,4A→∅

Abstract

Phase transitions of the 2A-->3A, 4A--> X reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations. The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the site mean-field approximation shows a single transition at zero branching rate introduced by Odor [G. Odor, Phys. Rev. E 67, 056114 (2003)], N>2 cluster approximations predict the appearance of another transition line for weak diffusion (D) as well. The latter phase transition is continuous, occurs at finite branching rate, and exhibits different scaling behavior. I show that the universal behavior of these transitions is in agreement with that of the diffusive pair contact process model both on the mean-field level and in one dimension. Therefore this model exhibiting annihilation by quadruplets does not fit in the recently suggested classification of universality classes of absorbing state transitions in one dimension [J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003)]. For high diffusion rates the effective 2A-->3A-->4A--> X reaction becomes irrelevant and the model exhibits a mean-field transition only. The two regions are separated by a nontrivial critical end point at D*.

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

“…This conjecture is in agreement with the observation of Ref. [42] that an additional parity-conservation does not change the critical behaviour of the PCPD (see [101] for recent evidence of a PCPD transition in the diffusive 2A → 3A, 4A → ∅ system, where m = 2, n = 4).…”

Cluster mean-field study of the parity-conserving phase transition

“…The interplay of diffusion and fluctuation has already been shown in many reaction-diffusion models (see for example [21,27,29,30]). Although the diffusion is unable to change the universal behavior it can affect the location of the transition and even more it can change the stability of a fixed point in case of competing reactions [27,29,30]). To investigate the possible role of diffusion we also extend the parameter space by modifying the diffusion rate.…”

“…It is well known that such approximations predict the phase structure qualitatively well in one dimension, provided N is large enough to take into account the relevant interaction terms. For example N > 1 is needed to take into account particle diffusion terms, while N > 2 was found to be necessary in case of binary production processes involving pair induced reactions [27,28]. The GMF is an efficient phase diagram exploration method and although it is set up for the d = 1 lattice in previous cases it provided qualitatively good phase diagram for higher dimensional, mean-field versions as well (see example [26,29,35,36]).…”

Population dynamics in the triplet annihilation model with a mutating reproduction rate

“…Katori and Konno [11] established some general properties of systems like the TAM, while Poland [12] used time-series expansions to investigate population dynamics in the TAM and related models. A model with annihilation of quadruplets was analyzed by Ódor [13,14].…”