The role of diffusion in branching and annihilation random walk models

Different branching and annihilating random walk models are investigated by cluster mean-field method and simulations in one and two dimensions. In case of the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by non-perturbative renormalization group method (L. Canet et al., cond-mat/0403423). The same type of survey for the A -> 2A, 4A -> 0 model results in a reentrant phase diagram, similar to that of 2A -> 3A, 4A -> 0 model (G. \'Odor, PRE {\bf 69}, 036112 (2004)). Simulations of the A -> 2A, 4A -> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.Comment: 4 pages, 4 figures, 1 table include

The phase transition of triplet reaction-diffusion models

The phase transitions classes of reaction-diffusion systems with multi-particle reactions is an open challenging problem. Large scale simulations are applied for the 3A -> 4A, 3A -> 2A and the 3A -> 4A, 3A->0 triplet reaction models with site occupation restriction in one dimension. Static and dynamic mean-field scaling is observed with signs of logarithmic corrections suggesting d_c=1 upper critical dimension for this family of models.Comment: 4 pages, 4 figures, updated version prior publication in PR

Non-equilibrium Anisotropic Phases, Nucleation and Critical Behavior in a Driven Lennard-Jones Fluid

We describe short-time kinetic and steady-state properties of the non--equilibrium phases, namely, solid, liquid and gas anisotropic phases in a driven Lennard-Jones fluid. This is a computationally-convenient two-dimensional model which exhibits a net current and striped structures at low temperature, thus resembling many situations in nature. We here focus on both critical behavior and details of the nucleation process. In spite of the anisotropy of the late--time spinodal decomposition process, earlier nucleation seems to proceed by Smoluchowski coagulation and Ostwald ripening, which are known to account for nucleation in equilibrium, isotropic lattice systems and actual fluids. On the other hand, a detailed analysis of the system critical behavior rises some intriguing questions on the role of symmetries; this concerns the computer and field-theoretical modeling of non-equilibrium fluids.Comment: 7 pages, 9 ps figures, to appear in PR

Theoretical Characterization of the Interface in a Nonequilibrium Lattice System

The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the familiar spin--flip dynamics at temperature T with completely--random flips; one may interpret these as ideally simulating some (dynamic) impurities. We find evidence that, in the present case, the nonequilibrium mechanism adds to the basic thermal one resulting on a renormalization of microscopic parameters such as the probability of interfacial broken bonds. On this assumption, we develop theory for the nonequilibrium "surface tension", which happens to show a non--monotonous behavior with a maximum at some finite T. It ensues, in full agreement with Monte Carlo simulations, that interface fluctuations differ qualitatively from the equilibrium case, e.g., the interface remains rough at zero--T. We discuss on some consequences of these facts for nucleation theory, and make some explicit predictions concerning the nonequilibrium droplet structure.Comment: 10 pages, 7 figures, submitted to Phys. Re

Critical behavior of the two dimensional 2A->3A, 4A->0 binary system

The phase transitions of the recently introduced 2A -> 3A, 4A -> 0 reaction-diffusion model (G.Odor, PRE 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 $\alpha=1/3$ density decay exponent. In contrast with this for weak diffusion the effective 2A ->3A->4A->0 reaction becomes relevant and the mean-field transition of the 2A -> 3A, 2A -> 0 model characterized by $\alpha=1/2$ also appears for non-zero branching rates.Comment: 5 pages, 5 figures included, small correction

Universality class of the pair contact process with diffusion

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2), beta=0.28(2) and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that PCPD falls in the same universality class as DP.Comment: 8 pages, 8 figures, accepted by Phys. Rev. E (not yet published

Probability distribution of the order parameter in the directed percolation universality class

The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the Domany-Kinzel cellular automaton. In both cases, the density of active sites was chosen as the order parameter. The criticality of those models was obtained by solely using the corresponding probability distribution function. It has been shown that the present method, which has been successfully employed in treating equilibrium systems, is indeed also useful in the study of nonequilibrium phase transitions.Comment: 6 pages, 4 figure

The phase transition of the diffusive pair contact process revisited

The restricted diffusive pair contact process 2A->3A, 2A->0 (PCPD) and the classification of its critical behavior continues to be a challenging open problem of non-equilibrium statistical mechanics. Recently Kockelkoren and Chate [Phys. Rev. Lett. 90, 125701 (2003)] suggested that the PCPD in one spatial dimension represents a genuine universality class of non-equilibrium phase transitions which differs from previously known classes. To this end they introduced an efficient lattice model in which the number of particles per site is unrestricted. In numerical simulations this model displayed clean power laws, indicating ordinary critical behavior associated with certain non-trivial critical exponents. In the present work, however, we arrive at a different conclusion. Increasing the numerical effort, we find a slow drift of the effective exponents which is of the same type as observed in previously studied fermionic realizations. Analyzing this drift we discuss the possibility that the asymptotic critical behavior of the PCPD may be governed by an ordinary directed percolation fixed point.Comment: 6 pages, 1 figur

Phase transitions for rock-scissors-paper game on different networks

Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and annealed randomness simultaneously. In the resulting phase diagrams three different stationary states are identified for all structures. The comparison of results on different networks suggests that the value of clustering coefficient plays an irrelevant role in the emergence of a global oscillating phase. The critical behavior of phase transitions seems to be universal and can be described by the same exponents.Comment: 4 pages, 4 figures, to be published in PR