1,748 research outputs found
Self-organized criticality and directed percolation
A sandpile model with stochastic toppling rule is studied. The control
parameters and the phase diagram are determined through a MF approach, the
subcritical and critical regions are analyzed. The model is found to have some
similarities with directed percolation, but the existence of different boundary
conditions and conservation law leads to a different universality class, where
the critical state is extended to a line segment due to self-organization.
These results are supported with numerical simulations in one dimension. The
present model constitute a simple model which capture the essential difference
between ordinary nonequilibrium critical phenomena, like DP, and self-organized
criticality.Comment: 9 pages, 10 eps figs, revtex, submitted to J. Phys.
Compact parity conserving percolation in one-dimension
Compact directed percolation is known to appear at the endpoint of the
directed percolation critical line of the Domany-Kinzel cellular automaton in
1+1 dimension. Equivalently, such transition occurs at zero temperature in a
magnetic field H, upon changing the sign of H, in the one-dimensional
Glauber-Ising model with well known exponents characterising spin-cluster
growth. We have investigated here numerically these exponents in the
non-equilibrium generalization (NEKIM) of the Glauber model in the vicinity of
the parity-conserving phase transition point of the kinks. Critical
fluctuations on the level of kinks are found to affect drastically the
characteristic exponents of spreading of spins while the hyperscaling relation
holds in its form appropriate for compact clusters.Comment: 7 pages, 7 figures embedded in the latex, final form before J.Phys.A
publicatio
The coil-globule transition of confined polymers
We study long polymer chains in a poor solvent, confined to the space between
two parallel hard walls. The walls are energetically neutral and pose only a
geometric constraint which changes the properties of the coil-globule (or
"-") transition. We find that the temperature increases
monotonically with the width between the walls, in contrast to recent
claims in the literature. Put in a wider context, the problem can be seen as a
dimensional cross over in a tricritical point of a model. We roughly
verify the main scaling properties expected for such a phenomenon, but we find
also somewhat unexpected very long transients before the asymptotic scaling
regions are reached. In particular, instead of the expected scaling exactly at the (-dependent) theta point we found that increases
less fast than , even for extremely long chains.Comment: 5 pages, 6 figure
Absorbing Phase Transitions of Branching-Annihilating Random Walks
The phase transitions to absorbing states of the branching-annihilating
reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied
systematically in one space dimension within a new family of models. Four
universality classes of non-trivial critical behavior are found. This provides,
in particular, the first evidence of universal scaling laws for pair and
triplet processes.Comment: 4 pages, 4 figure
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
Simulations of grafted polymers in a good solvent
We present improved simulations of three-dimensional self avoiding walks with
one end attached to an impenetrable surface on the simple cubic lattice. This
surface can either be a-thermal, having thus only an entropic effect, or
attractive. In the latter case we concentrate on the adsorption transition, We
find clear evidence for the cross-over exponent to be smaller than 1/2, in
contrast to all previous simulations but in agreement with a re-summed field
theoretic -expansion. Since we use the pruned-enriched Rosenbluth
method (PERM) which allows very precise estimates of the partition sum itself,
we also obtain improved estimates for all entropic critical exponents.Comment: 5 pages with 9 figures included; minor change
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
Correlated Initial Conditions in Directed Percolation
We investigate the influence of correlated initial conditions on the temporal
evolution of a (d+1)-dimensional critical directed percolation process.
Generating initial states with correlations ~r^(sigma-d) we
observe that the density of active sites in Monte-Carlo simulations evolves as
rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in
the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an
exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure
Directed Percolation with a Wall or Edge
We examine the effects of introducing a wall or edge into a directed
percolation process. Scaling ansatzes are presented for the density and
survival probability of a cluster in these geometries, and we make the
connection to surface critical phenomena and field theory. The results of
previous numerical work for a wall can thus be interpreted in terms of surface
exponents satisfying scaling relations generalising those for ordinary directed
percolation. New exponents for edge directed percolation are also introduced.
They are calculated in mean-field theory and measured numerically in 2+1
dimensions.Comment: 14 pages, submitted to J. Phys.
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