574 research outputs found
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 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 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
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