1,760 research outputs found
Pair Connectedness and Shortest Path Scaling in Critical Percolation
We present high statistics data on the distribution of shortest path lengths
between two near-by points on the same cluster at the percolation threshold.
Our data are based on a new and very efficient algorithm. For they
clearly disprove a recent conjecture by M. Porto et al., Phys. Rev. {\bf E 58},
R5205 (1998). Our data also provide upper bounds on the probability that two
near-by points are on different infinite clusters.Comment: 7 pages, including 4 postscript figure
Critical Behaviour of the Drossel-Schwabl Forest Fire Model
We present high statistics Monte Carlo results for the Drossel-Schwabl forest
fire model in 2 dimensions. They extend to much larger lattices (up to
) than previous simulations and reach much closer to the
critical point (up to ). They are incompatible with
all previous conjectures for the (extrapolated) critical behaviour, although
they in general agree well with previous simulations wherever they can be
directly compared. Instead, they suggest that scaling laws observed in previous
simulations are spurious, and that the density of trees in the critical
state was grossly underestimated. While previous simulations gave , we conjecture that actually is equal to the critical threshold
for site percolation in . This is however still far from
the densities reachable with present day computers, and we estimate that we
would need many orders of magnitude higher CPU times and storage capacities to
reach the true critical behaviour -- which might or might not be that of
ordinary percolation.Comment: 8 pages, including 9 figures, RevTe
Epidemic analysis of the second-order transition in the Ziff-Gulari-Barshad surface-reaction model
We study the dynamic behavior of the Ziff-Gulari-Barshad (ZGB) irreversible
surface-reaction model around its kinetic second-order phase transition, using
both epidemic and poisoning-time analyses. We find that the critical point is
given by p_1 = 0.3873682 \pm 0.0000015, which is lower than the previous value.
We also obtain precise values of the dynamical critical exponents z, \delta,
and \eta which provide further numerical evidence that this transition is in
the same universality class as directed percolation.Comment: REVTEX, 4 pages, 5 figures, Submitted to Physical Review
Comment on "Dynamic Opinion Model and Invasion Percolation"
In J. Shao et al., PRL 103, 108701 (2009) the authors claim that a model with
majority rule coarsening exhibits in d=2 a percolation transition in the
universality class of invasion percolation with trapping. In the present
comment we give compelling evidence, including high statistics simulations on
much larger lattices, that this is not correct. and that the model is trivially
in the ordinary percolation universality class.Comment: 1 pag
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
Kinetic induced phase transition
An Ising model with local Glauber dynamics is studied under the influence of
additional kinetic restrictions for the spin-flip rates depending on the
orientation of neighboring spins. Even when the static interaction between the
spins is completely eliminated and only an external field is taken into account
the system offers a phase transition at a finite value of the applied field.
The transition is realized due to a competition between the activation
processes driven by the field and the dynamical rules for the spin-flips. The
result is based on a master equation approach in a quantum formulation.Comment: 13 page
Damage Spreading in the Ising Model
We present two new results regarding damage spreading in ferromagnetic Ising
models. First, we show that a damage spreading transition can occur in an Ising
chain that evolves in contact with a thermal reservoir. Damage heals at low
temperature and spreads for high T. The dynamic rules for the system's
evolution for which such a transition is observed are as legitimate as the
conventional rules (Glauber, Metropolis, heat bath). Our second result is that
such transitions are not always in the directed percolation universality class.Comment: 5 pages, RevTeX, revised and extended version, including 3 postscript
figure
Chaotic synchronizations of spatially extended systems as non-equilibrium phase transitions
Two replicas of spatially extended chaotic systems synchronize to a common
spatio-temporal chaotic state when coupled above a critical strength. As a
prototype of each single spatio-temporal chaotic system a lattice of maps
interacting via power-law coupling is considered. The synchronization
transition is studied as a non-equilibrium phase transition, and its critical
properties are analyzed at varying the spatial interaction range as well as the
nonlinearity of the dynamical units composing each system. In particular,
continuous and discontinuous local maps are considered. In both cases the
transitions are of the second order with critical indexes varying with the
exponent characterizing the interaction range. For discontinuous maps it is
numerically shown that the transition belongs to the {\it anomalous directed
percolation} (ADP) family of universality classes, previously identified for
L{\'e}vy-flight spreading of epidemic processes. For continuous maps, the
critical exponents are different from those characterizing ADP, but apart from
the nearest-neighbor case, the identification of the corresponding universality
classes remains an open problem. Finally, to test the influence of
deterministic correlations for the studied synchronization transitions, the
chaotic dynamical evolutions are substituted by suitable stochastic models. In
this framework and for the discontinuous case, it is possible to derive an
effective Langevin description that corresponds to that proposed for ADP.Comment: 12 pages, 5 figures Comments are welcom
Epidemic spreading with immunization and mutations
The spreading of infectious diseases with and without immunization of
individuals can be modeled by stochastic processes that exhibit a transition
between an active phase of epidemic spreading and an absorbing phase, where the
disease dies out. In nature, however, the transmitted pathogen may also mutate,
weakening the effect of immunization. In order to study the influence of
mutations, we introduce a model that mimics epidemic spreading with
immunization and mutations. The model exhibits a line of continuous phase
transitions and includes the general epidemic process (GEP) and directed
percolation (DP) as special cases. Restricting to perfect immunization in two
spatial dimensions we analyze the phase diagram and study the scaling behavior
along the phase transition line as well as in the vicinity of the GEP point. We
show that mutations lead generically to a crossover from the GEP to DP. Using
standard scaling arguments we also predict the form of the phase transition
line close to the GEP point. It turns out that the protection gained by
immunization is vitally decreased by the occurrence of mutations.Comment: 9 pages, 13 figure
Systematic Series Expansions for Processes on Networks
We use series expansions to study dynamics of equilibrium and non-equilibrium
systems on networks. This analytical method enables us to include detailed
non-universal effects of the network structure. We show that even low order
calculations produce results which compare accurately to numerical simulation,
while the results can be systematically improved. We show that certain commonly
accepted analytical results for the critical point on networks with a broad
degree distribution need to be modified in certain cases due to
disassortativity; the present method is able to take into account the
assortativity at sufficiently high order, while previous results correspond to
leading and second order approximations in this method. Finally, we apply this
method to real-world data.Comment: 4 pages, 3 figure
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