236 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
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
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
Rare regions of the susceptible-infected-susceptible model on Barabási-Albert networks
I extend a previous work to susceptible-infected-susceptible (SIS) models on weighted Barabási-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 ∼0.25, 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 ρ(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
Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
The octahedron model introduced recently has been implemented onto graphics
cards, which permits extremely large scale simulations via binary lattice gases
and bit coded algorithms. We confirm scaling behaviour belonging to the 2d
Kardar-Parisi-Zhang universality class and find a surface growth exponent:
beta=0.2415(15) on 2^17 x 2^17 systems, ruling out beta=1/4 suggested by field
theory. The maximum speed-up with respect to a single CPU is 240. The steady
state has been analysed by finite size scaling and a growth exponent
alpha=0.393(4) is found. Correction to scaling exponents are computed and the
power-spectrum density of the steady state is determined. We calculate the
universal scaling functions, cumulants and show that the limit distribution can
be obtained by the sizes considered. We provide numerical fitting for the small
and large tail behaviour of the steady state scaling function of the interface
width.Comment: 7 pages, 8 figures, slightly modified, accepted version for PR
One-dimensional spin-anisotropic kinetic Ising model subject to quenched disorder
Large-scale Monte Carlo simulations are used to explore the effect of
quenched disorder on one dimensional, non-equilibrium kinetic Ising models with
locally broken spin symmetry, at zero temperature (the symmetry is broken
through spin-flip rates that differ for '+' and '-' spins). The model is found
to exhibit a continuous phase transition to an absorbing state. The associated
critical behavior is studied at zero branching rate of kinks, through analysis
spreading of '+' and '-' spins and, of the kink density. Impurities exert a
strong effect on the critical behavior only for a particular choice of
parameters, corresponding to the strongly spin-anisotropic kinetic Ising model
introduced by Majumdar et al. Typically, disorder effects become evident for
impurity strengths such that diffusion is nearly blocked. In this regime, the
critical behavior is similar to that arising, for example, in the
one-dimensional diluted contact process, with Griffiths-like behavior for the
kink density. We find variable cluster exponents, which obey a hyperscaling
relation, and are similar to those reported by Cafiero et al. We also show that
the isotropic two-component AB -> 0 model is insensitive to reaction-disorder,
and that only logarithmic corrections arise, induced by strong disorder in the
diffusion rate.Comment: 10 pages, 13 figures. Final, accepted form in PRE, including a new
table summarizing the molde
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
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
Slow dynamics and rare-region effects in the contact process on weighted tree networks
We show that generic, slow dynamics can occur in the contact process on
complex networks with a tree-like structure and a superimposed weight pattern,
in the absence of additional (non-topological) sources of quenched disorder.
The slow dynamics is induced by rare-region effects occurring on correlated
subspaces of vertices connected by large weight edges, and manifests in the
form of a smeared phase transition. We conjecture that more sophisticated
network motifs could be able to induce Griffiths phases, as a consequence of
purely topological disorder.Comment: 12 pages, 10 figures, final version appeared in PR
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