92 research outputs found
Infinite-randomness critical point in the two-dimensional disordered contact process
We study the nonequilibrium phase transition in the two-dimensional contact
process on a randomly diluted lattice by means of large-scale Monte-Carlo
simulations for times up to and system sizes up to
sites. Our data provide strong evidence for the transition being controlled by
an exotic infinite-randomness critical point with activated (exponential)
dynamical scaling. We calculate the critical exponents of the transition and
find them to be universal, i.e., independent of disorder strength. The
Griffiths region between the clean and the dirty critical points exhibits
power-law dynamical scaling with continuously varying exponents. We discuss the
generality of our findings and relate them to a broader theory of rare region
effects at phase transitions with quenched disorder. Our results are of
importance beyond absorbing state transitions because according to a
strong-disorder renormalization group analysis, our transition belongs to the
universality class of the two-dimensional random transverse-field Ising model.Comment: 13 pages, 12 eps figures, final version as publishe
Weakly disordered absorbing-state phase transitions
The effects of quenched disorder on nonequilibrium phase transitions in the
directed percolation universality class are revisited. Using a strong-disorder
energy-space renormalization group, it is shown that for any amount of disorder
the critical behavior is controlled by an infinite-randomness fixed point in
the universality class of the random transverse-field Ising models. The
experimental relevance of our results are discussed.Comment: 4 pages, 2 eps figures; (v2) references and discussion on experiments
added; (v3) published version, minor typos corrected, some side discussions
dropped due to size constrain
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
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
Broadening of a nonequilibrium phase transition by extended structural defects
We study the effects of quenched extended impurities on nonequilibrium phase
transitions in the directed percolation universality class. We show that these
impurities have a dramatic effect: they completely destroy the sharp phase
transition by smearing. This is caused by rare strongly coupled spatial regions
which can undergo the phase transition independently from the bulk system. We
use extremal statistics to determine the stationary state as well as the
dynamics in the tail of the smeared transition, and we illustrate the results
by computer simulations.Comment: 4 pages, 4 eps figures, final version as publishe
Critical behavior and Griffiths effects in the disordered contact process
We study the nonequilibrium phase transition in the one-dimensional contact
process with quenched spatial disorder by means of large-scale Monte-Carlo
simulations for times up to and system sizes up to sites. In
agreement with recent predictions of an infinite-randomness fixed point, our
simulations demonstrate activated (exponential) dynamical scaling at the
critical point. The critical behavior turns out to be universal, even for weak
disorder. However, the approach to this asymptotic behavior is extremely slow,
with crossover times of the order of or larger. In the Griffiths region
between the clean and the dirty critical points, we find power-law dynamical
behavior with continuously varying exponents. We discuss the generality of our
findings and relate them to a broader theory of rare region effects at phase
transitions with quenched disorder.Comment: 10 pages, 8 eps figures, final version as publishe
First Passage Time in a Two-Layer System
As a first step in the first passage problem for passive tracer in stratified
porous media, we consider the case of a two-dimensional system consisting of
two layers with different convection velocities. Using a lattice generating
function formalism and a variety of analytic and numerical techniques, we
calculate the asymptotic behavior of the first passage time probability
distribution. We show analytically that the asymptotic distribution is a simple
exponential in time for any choice of the velocities. The decay constant is
given in terms of the largest eigenvalue of an operator related to a half-space
Green's function. For the anti-symmetric case of opposite velocities in the
layers, we show that the decay constant for system length crosses over from
behavior in diffusive limit to behavior in the convective
regime, where the crossover length is given in terms of the velocities.
We also have formulated a general self-consistency relation, from which we have
developed a recursive approach which is useful for studying the short time
behavior.Comment: LaTeX, 28 pages, 7 figures not include
Strong disorder fixed point in absorbing state phase transitions
The effect of quenched disorder on non-equilibrium phase transitions in the
directed percolation universality class is studied by a strong disorder
renormalization group approach and by density matrix renormalization group
calculations. We show that for sufficiently strong disorder the critical
behaviour is controlled by a strong disorder fixed point and in one dimension
the critical exponents are conjectured to be exact: \beta=(3-\sqrt{5})/2 and
\nu_\perp=2. For disorder strengths outside the attractive region of this fixed
point, disorder dependent critical exponents are detected. Existing numerical
results in two dimensions can be interpreted within a similar scenario.Comment: final version as accepted for PRL, contains new results in two
dimension
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