229 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
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
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
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 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 novel 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 Park et al.'s recent study (Phys. Rev E {\bf
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 1d show robust, non-trivial transitions
suggesting d_c=2. Furthermore I show that a parity conserving model 3A -> 5A,
2A->0 in d=1 has a continuous phase transition with novel kind 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 Chat\'e
(cond-mat/0208497).Comment: 8 pages, 10 figures included, Updated with new data, figures, table,
to be published in PR
Phase transition of the one-dimensional coagulation-production process
Recently an exact solution has been found (M.Henkel and H.Hinrichsen,
cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A
with equal diffusion and coagulation rates. This model evolves into the
inactive phase independently of the production rate with density
decay law. Here I show that cluster mean-field approximations and Monte Carlo
simulations predict a continuous phase transition for higher
diffusion/coagulation rates as considered in cond-mat/0010062. Numerical
evidence is given that the phase transition universality agrees with that of
the annihilation-fission model with low diffusions.Comment: 4 pages, 4 figures include
Rare regions of the susceptible-infected-susceptible model on BarabĂĄsi-Albert networks
I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted BarabĂĄsi-Albert scale-free networks. Numerical evidence is provided that phases with slow, power-law dynamics emerge as the consequence of quenched disorder and tree topologies studied previously with the contact process. I compare simulation results with spectral analysis of the networks and show that the quenched mean-field (QMF) approximation provides a reliable, relatively fast method to explore activity clustering. This suggests that QMF can be used for describing rare-region effects due to network inhomogeneities. Finite-size study of the QMF shows the expected disappearance of the epidemic threshold λc in the thermodynamic limit and an inverse participation ratio âŒ0.25, meaning localization in case of disassortative weight scheme. Contrarily, for the multiplicative weights and the unweighted trees, this value vanishes in the thermodynamic limit, suggesting only weak rare-region effects in agreement with the dynamical simulations. Strong corrections to the mean-field behavior in case of disassortative weights explains the concave shape of the order parameter Ï(λ) at the transition point. Application of this method to other models may reveal interesting rare-region effects, Griffiths phases as the consequence of quenched topological heterogeneities
Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.
The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod.
Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly
method. Reliable estimate was found for the critical exponent, based on
moderate sized () clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]
Scaling behavior of the contact process in networks with long-range connections
We present simulation results for the contact process on regular, cubic
networks that are composed of a one-dimensional lattice and a set of long edges
with unbounded length. Networks with different sets of long edges are
considered, that are characterized by different shortest-path dimensions and
random-walk dimensions. We provide numerical evidence that an absorbing phase
transition occurs at some finite value of the infection rate and the
corresponding dynamical critical exponents depend on the underlying network.
Furthermore, the time-dependent quantities exhibit log-periodic oscillations in
agreement with the discrete scale invariance of the networks. In case of
spreading from an initial active seed, the critical exponents are found to
depend on the location of the initial seed and break the hyper-scaling law of
the directed percolation universality class due to the inhomogeneity of the
networks. However, if the cluster spreading quantities are averaged over
initial sites the hyper-scaling law is restored.Comment: 9 pages, 10 figure
One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation 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 for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR
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 (). We found
that cluster mean-field approximations must be considered to get
consistent singular behavior. The approximations result in a continuous
phase transition belonging to a single universality class along the 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 that the upper critical dimension
in this model is .The pair density scales in a similar way but with an
additional logarithmic factor to the order parameter. At the D=0 endpoint of
the transition line we found DP criticality.Comment: 8 pages, 10 figure
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