14,285 research outputs found
Field theory of directed percolation with long-range spreading
It is well established that the phase transition between survival and
extinction in spreading models with short-range interactions is generically
associated with the directed percolation (DP) universality class. In many
realistic spreading processes, however, interactions are long ranged and well
described by L\'{e}vy-flights, i.e., by a probability distribution that decays
in dimensions with distance as . We employ the powerful
methods of renormalized field theory to study DP with such long range,
L\'{e}vy-flight spreading in some depth. Our results unambiguously corroborate
earlier findings that there are four renormalization group fixed points
corresponding to, respectively, short-range Gaussian, L\'{e}vy Gaussian,
short-range DP and L\'{e}vy DP, and that there are four lines in the plane which separate the stability regions of these fixed points. When the
stability line between short-range DP and L\'{e}vy DP is crossed, all critical
exponents change continuously. We calculate the exponents describing L\'{e}vy
DP to second order in -expansion, and we compare our analytical
results to the results of existing numerical simulations. Furthermore, we
calculate the leading logarithmic corrections for several dynamical
observables.Comment: 12 pages, 3 figure
Finite-size scaling of directed percolation above the upper critical dimension
We consider analytically as well as numerically the finite-size scaling
behavior in the stationary state near the non-equilibrium phase transition of
directed percolation within the mean field regime, i.e., above the upper
critical dimension. Analogous to equilibrium, usual finite-size scaling is
valid below the upper critical dimension, whereas it fails above. Performing a
momentum analysis of associated path integrals we derive modified finite-size
scaling forms of the order parameter and its higher moments. The results are
confirmed by numerical simulations of corresponding high-dimensional lattice
models.Comment: 4 pages, one figur
A Generalized Epidemic Process and Tricritical Dynamic Percolation
The renowned general epidemic process describes the stochastic evolution of a
population of individuals which are either susceptible, infected or dead. A
second order phase transition belonging to the universality class of dynamic
isotropic percolation lies between endemic or pandemic behavior of the process.
We generalize the general epidemic process by introducing a fourth kind of
individuals, viz. individuals which are weakened by the process but not yet
infected. This sensibilization gives rise to a mechanism that introduces a
global instability in the spreading of the process and therefore opens the
possibility of a discontinuous transition in addition to the usual continuous
percolation transition. The tricritical point separating the lines of first and
second order transitions constitutes a new universality class, namely the
universality class of tricritical dynamic isotropic percolation. Using
renormalized field theory we work out a detailed scaling description of this
universality class. We calculate the scaling exponents in an
-expansion below the upper critical dimension for various
observables describing tricritical percolation clusters and their spreading
properties. In a remarkable contrast to the usual percolation transition, the
exponents and governing the two order parameters,
viz. the mean density and the percolation probability, turn out to be different
at the tricritical point. In addition to the scaling exponents we calculate for
all our static and dynamic observables logarithmic corrections to the
mean-field scaling behavior at .Comment: 21 pages, 10 figures, version to appear in Phys. Rev.
Finite-size scaling of directed percolation in the steady state
Recently, considerable progress has been made in understanding finite-size
scaling in equilibrium systems. Here, we study finite-size scaling in
non-equilibrium systems at the instance of directed percolation (DP), which has
become the paradigm of non-equilibrium phase transitions into absorbing states,
above, at and below the upper critical dimension. We investigate the
finite-size scaling behavior of DP analytically and numerically by considering
its steady state generated by a homogeneous constant external source on a
d-dimensional hypercube of finite edge length L with periodic boundary
conditions near the bulk critical point. In particular, we study the order
parameter and its higher moments using renormalized field theory. We derive
finite-size scaling forms of the moments in a one-loop calculation. Moreover,
we introduce and calculate a ratio of the order parameter moments that plays a
similar role in the analysis of finite size scaling in absorbing nonequilibrium
processes as the famous Binder cumulant in equilibrium systems and that, in
particular, provides a new signature of the DP universality class. To
complement our analytical work, we perform Monte Carlo simulations which
confirm our analytical results.Comment: 21 pages, 6 figure
Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process
A general field theoretic model of directed percolation with many colors that
is equivalent to a population model (Gribov process) with many species near
their extinction thresholds is presented. It is shown that the multicritical
behavior is always described by the well known exponents of Reggeon field
theory. In addition this universal model shows an instability that leads in
general to a total asymmetry between each pair of species of a cooperative
society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte
Short-time Critical Dynamics of the 3-Dimensional Ising Model
Comprehensive Monte Carlo simulations of the short-time dynamic behaviour are
reported for the three-dimensional Ising model at criticality. Besides the
exponent of the critical initial increase and the dynamic exponent
, the static critical exponents and as well as the critical
temperature are determined from the power-law scaling behaviour of observables
at the beginning of the time evolution. States of very high temperature as well
as of zero temperature are used as initial states for the simulations.Comment: 8 pages with 7 figure
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
Forces on Bins - The Effect of Random Friction
In this note we re-examine the classic Janssen theory for stresses in bins,
including a randomness in the friction coefficient. The Janssen analysis relies
on assumptions not met in practice; for this reason, we numerically solve the
PDEs expressing balance of momentum in a bin, again including randomness in
friction.Comment: 11 pages, LaTeX, with 9 figures encoded, gzippe
Quantized charge pumping through a quantum dot by surface acoustic waves
We present a realization of quantized charge pumping. A lateral quantum dot
is defined by metallic split gates in a GaAs/AlGaAs heterostructure. A surface
acoustic wave whose wavelength is twice the dot length is used to pump single
electrons through the dot at a frequency f=3GHz. The pumped current shows a
regular pattern of quantization at values I=nef over a range of gate voltage
and wave amplitude settings. The observed values of n, the number of electrons
transported per wave cycle, are determined by the number of electronic states
in the quantum dot brought into resonance with the fermi level of the electron
reservoirs during the pumping cycle.Comment: 8 page
Localization of Multi-Dimensional Wigner Distributions
A well known result of P. Flandrin states that a Gaussian uniquely maximizes
the integral of the Wigner distribution over every centered disc in the phase
plane. While there is no difficulty in generalizing this result to
higher-dimensional poly-discs, the generalization to balls is less obvious. In
this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic
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