140 research outputs found
Non-Markovian Persistence at the PC point of a 1d non-equilibrium kinetic Ising model
One-dimensional non-equilibrium kinetic Ising models evolving under the
competing effect of spin flips at zero temperature and nearest neighbour spin
exchanges exhibiting a parity-conserving (PC) phase transition on the level of
kinks are investigated here numerically from the point of view of the
underlying spin system. The dynamical persistency exponent and the
exponent characterising the two-time autocorrelation function of the
total magnetization under non-equilibrium conditions are reported. It is found
that the PC transition has strong effect: the process becomes non-Markovian and
the above exponents exhibit drastic changes as compared to the Glauber-Ising
case.Comment: 6 pages, Latex, postscript figures include
Local scale invariance in the parity conserving nonequilibrium kinetic Ising model
The local scale invariance has been investigated in the nonequilibrium
kinetic Ising model exhibiting absorbing phase transition of PC type in 1+1
dimension. Numerical evidence has been found for the satisfaction of this
symmetry and estimates for the critical ageing exponents are given.Comment: 8 pages, 2 figures (IOP format), final form to appear in JSTA
Phase transitions and critical behaviour in one-dimensional non-equilibrium kinetic Ising models with branching annihilating random walk of kinks
One-dimensional non-equilibrium kinetic Ising models evolving under the
competing effect of spin flips at zero temperature and nearest-neighbour spin
exchanges exhibiting directed percolation-like parity conserving(PC) phase
transition on the level of kinks are now further investigated, numerically,
from the point of view of the underlying spin system. Critical exponents
characterising its statics and dynamics are reported. It is found that the
influence of the PC transition on the critical exponents of the spins is strong
and the origin of drastic changes as compared to the Glauber-Ising case can be
traced back to the hyperscaling law stemming from directed percolation(DP).
Effect of an external magnetic field, leading to DP-type critical behaviour on
the level of kinks, is also studied, mainly through the generalised mean field
approximation.Comment: 15 pages, using RevTeX, 13 Postscript figures included, submitted to
J.Phys.A, figures 12 and 13 fixe
The three species monomer-monomer model in the reaction-controlled limit
We study the one dimensional three species monomer-monomer reaction model in
the reaction controlled limit using mean-field theory and dynamic Monte Carlo
simulations. The phase diagram consists of a reactive steady state bordered by
three equivalent adsorbing phases where the surface is saturated with one
monomer species. The transitions from the reactive phase are all continuous,
while the transitions between adsorbing phases are first-order. Bicritical
points occur where the reactive phase simultaneously meets two adsorbing
phases. The transitions from the reactive to an adsorbing phase show directed
percolation critical behaviour, while the universal behaviour at the bicritical
points is in the even branching annihilating random walk class. The results are
contrasted and compared to previous results for the adsorption-controlled limit
of the same model.Comment: 12 pages using RevTeX, plus 4 postscript figures. Uses psfig.sty.
accepted to Journal of Physics
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
Critical behaviour of annihilating random walk of two species with exclusion in one dimension
The , process with exclusion between the different
kinds is investigated here numerically. Before treating this model explicitly,
we study the generalized Domany-Kinzel cellular automaton model of Hinrichsen
on the line of the parameter space where only compact clusters can grow. The
simplest version is treated with two absorbing phases in addition to the active
one. The two kinds of kinks which arise in this case do not react, leading to
kinetics differing from standard annihilating random walk of two species. Time
dependent simulations are presented here to illustrate the differences caused
by exclusion in the scaling properties of usually discussed characteristic
quantities. The dependence on the density and composition of the initial state
is most apparent. Making use of the parallelism between this process and
directed percolation limited by a reflecting parabolic surface we argue that
the two kinds of kinks exert marginal perturbation on each other leading to
deviations from standard annihilating random walk behavior.Comment: 12 pages, 16 figures, small typos corrected, 2 references adde
Crossovers from parity conserving to directed percolation universality
The crossover behavior of various models exhibiting phase transition to
absorbing phase with parity conserving class has been investigated by numerical
simulations and cluster mean-field method. In case of models exhibiting Z_2
symmetric absorbing phases (the NEKIMCA and Grassberger's A stochastic cellular
automaton) the introduction of an external symmetry breaking field causes a
crossover to kink parity conserving models characterized by dynamical scaling
of the directed percolation (DP) and the crossover exponent: 1/\phi ~ 0.53(2).
In case an even offspringed branching and annihilating random walk model (dual
to NEKIMCA) the introduction of spontaneous particle decay destroys the parity
conservation and results in a crossover to the DP class characterized by the
crossover exponent: 1/\phi\simeq 0.205(5). The two different kinds of crossover
operators can't be mapped onto each other and the resulting models show a
diversity within the DP universality class in one dimension. These
'sub-classes' differ in cluster scaling exponents.Comment: 6 pages, 6 figures, accepted version in PR
Non-equilibrium phase transitions in one-dimensional kinetic Ising models
A family of nonequilibrium kinetic Ising models, introduced earlier, evolving
under the competing effect of spin flips at {\it zero temperature} and nearest
neighbour random spin exchanges is further investigated here. By increasing the
range of spin exchanges and/or their strength the nature of the phase
transition 'Ising-to-active' becomes of (dynamic) mean-field type and a first
order tricitical point is located at the Glauber () limit.
Corrections to mean-field theory are evaluated up to sixth order in a cluster
approximation and found to give good results concerning the phase boundary and
the critical exponent of the order parameter which is obtained as
.Comment: 15 pages, revtex file, figures available at request from
[email protected] in postscript format, submitted to J.Phys.
Scratching resistance of SiC-rich nano-coatings produced by noble gas ion mixing
SiC-rich nano-layers were produced at room temperature by applying ion beam mixing of various C/Si multilayer structures using argon and xenon ions with energy in the range of 40–120 keV and fluences between 0.25 and 3 × 1016 ions/cm2. The mechanical behavior of the layers was characterized by scratch test. The scratching resistance of the ion mixed samples has been measured by standard scratch test applying an atomic-force microscope with a diamond-coated tip (radius < 15 nm) and they were compared to that measured on Si single crystal. The applied load varied in the range of 4–18 μN. The scratching resistance of the samples correlated with the effective areal density of the SiC; with increasing effective areal density the scratch depth decreases. Above sufficiently high effective areal density of SiC the scratch resistance (hardness) of the produced layer was somewhat higher than that of single crystal silicon. Previously it has been shown that such layers have excellent corrosion resistive properties as well. These findings allow to tune and design the mechanical and chemical properties of the SiC protective coatings
Damage spreading for one-dimensional, non-equilibrium models with parity conserving phase transitions
The damage spreading (DS) transitions of two one-dimensional stochastic
cellular automata suggested by Grassberger (A and B) and the kinetic Ising
model of Menyh\'ard (NEKIM) have been investigated on the level of kinks and
spins. On the level of spins the parity conservation is not satisfied and
therefore studying these models provides a convenient tool to understand the
dependence of DS properties on symmetries. For the model B the critical point
and the DS transition point is well separated and directed percolation damage
spreading transition universality was found for spin damage as well as for kink
damage in spite of the conservation of damage variables modulo 2 in the latter
case. For the A stochastic cellular automaton, and the NEKIM model the two
transition points coincide with drastic effects on the damage of spin and kink
variables showing different time dependent behaviours. While the kink DS
transition is continuous and shows regular PC class universality, the spin
damage exhibits a discontinuous phase transition with compact clusters and PC
like dynamical scaling (), () and () exponents whereas
the static exponents determined by FSS are consistent with that of the spins of
the NEKIM model at the PC transition point. The generalised hyper-scaling law
is satisfied.Comment: 11 pages, 20 figures embedded in the text, minor changes in the text,
a new table and new references are adde
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