Multicomponent binary spreading process

Coupled two-species model for the pair contact process with diffusion

The contact process with diffusion (PCPD) defined by the binary reactions B+B→B+B+B, B+B→∅ and diffusive particle spreading exhibits an unusual active to absorbing phase transition whose universality class has long been disputed. Multiple studies have indicated that an explicit account of particle pair degrees of freedom may be required to properly capture this system's effective long-time, large-scale behavior. We introduce a two-species representation for the PCPD in which single particles B and particle pairs A are dynamically coupled according to the stochastic reaction processes B+B→A, A→A+B, A→∅, and A→B+B, with each particle type diffusing independently. Mean-field analysis reveals that the phase transition of this model is driven by competition and balance between the two species. We employ Monte Carlo simulations in one, two, and three dimensions to demonstrate that this model consistently captures the pertinent features of the PCPD. In the inactive phase, A particles rapidly go extinct, effectively leaving the B species to undergo pure diffusion-limited pair annihilation kinetics B+B→∅. At criticality, both A and B densities decay with the same exponents (within numerical errors) as the corresponding order parameters of the original PCPD, and display mean-field scaling above the upper critical dimension d_{c}=2. In one dimension, the critical exponents for the B species obtained from seed simulations also agree well with previously reported exponent value ranges. We demonstrate that the scaling properties of consecutive particle pairs in the PCPD are identical with that of the A species in the coupled model. This two-species picture resolves the conceptual difficulty for seed simulations in the original PCPD and naturally introduces multiple length scales and timescales to the system, which are also the origin of strong corrections to scaling. The extracted moment ratios from our simulations indicate that our model displays the same temporal crossover behavior as the PCPD, which further corroborates its full dynamical equivalence with our coupled model.

Finite-scale singularity in the renormalization group flow of a reaction-diffusion system

We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a different (conjugated) universality class.

Critical behavior of nonequilibrium continuous phase transition in A+BC catalytic reaction system

We study two lattice gas models for the A+BC-->AC+ 1/2 B2 reaction system. Model I includes the influences of the adsorbate diffusion and model II includes the effect of the diffusion and position exchange of B and C atoms. Model I exhibits a continuous phase transition with infinitely many absorbing states from a reactive state to a poisoned state of B and C atoms and a discontinuous transition to a poisoned state of A and B atoms when the fraction of A in the gas phase varies. The critical exponents are estimated accurately. The simulation results indicate clearly that the critical behavior of the continuous phase transition in model I belongs to the directed percolation (DP) universality class. Model II, however, exhibits a continuous transition with two absorbing states, and its critical behavior is obviously distinct from the DP universality class.

Critical behavior of the two-dimensional 2A-->3A, 4A--> phi binary system

The phase transitions of the recently introduced 2A-->3A, 4A--> phi reaction-diffusion model [G. Odor, Phys. Rev. E 69, 036112 (2004)]] are explored in two dimensions. This model exhibits site-occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion-creation rate space is confirmed, in agreement with cluster mean-field and one-dimensional results. For strong diffusion, a mean-field transition can be observed at zero branching rate characterized by an alpha=1/3 density decay exponent. In contrast, for weak diffusion the effective 2A-->3A-->4A--> phi reaction becomes relevant and the mean-field transition of the 2A-->3A, 2A--> phi model characterized by alpha=1/2 also appears for nonzero branching rates.

Phase transitions of the binary production 2A-->3A, 4A--> X model

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*.

Phase transition classes in triplet and quadruplet reaction-diffusion models

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by the mean-field approximation and simulations. The mean-field approximation of general nA-->(n+k)A, mA-->(m-l)A type of lattice models is solved and a different kind of critical behavior is pointed out. In d=2 dimensions, the 3A-->4A, 3A-->2A model exhibits a continuous mean-field type of phase transition, that implies d(c)<2 upper critical dimension. For this model in d=1 extensive simulations support a mean-field type of phase transition with logarithmic corrections unlike the recent study of Park et al. [Phys. Rev E 66, 025101 (2002)]. On the other hand, the 4A-->5A, 4A-->3A quadruplet model exhibits a mean-field type of phase transition with logarithmic corrections in d=2, while quadruplet models in one-dimensional show robust, nontrivial transitions suggesting d(c)=2. Furthermore, I show that a parity conserving model 3A-->5A, 2A--> zero in d=1 has a continuous phase transition with different kinds of exponents. These results are in contradiction with the recently suggested implications of a phenomenological, multiplicative noise Langevin equation approach and with the simulations on suppressed bosonic systems by Kockelkoren and Chaté [Phys. Rev. Lett. 90, 125701 (2003)].

One-dimensional nonequilibrium kinetic Ising models with local spin symmetry breaking: N-component branching annihilating random-walk transition at zero branching rate

The effects of locally broken spin symmetry are investigated in one-dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster-mean-field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed.

Phase transition of a two-dimensional binary spreading model

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths (D). We found that N>2 cluster mean-field approximations must be considered to get consistent singular behavior. The N=3,4 approximations result in a continuous phase transition belonging to a single universality class along the D subset (0,1) phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting the bosonic field theoretical prediction that the upper critical dimension in this model is d(c)=2. The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D=0 end point of the transition line we found directed percolation criticality.