70 research outputs found
Global Persistence in Directed Percolation
We consider a directed percolation process at its critical point. The
probability that the deviation of the global order parameter with respect to
its average has not changed its sign between 0 and t decays with t as a power
law. In space dimensions d<4 the global persistence exponent theta_p that
characterizes this decay is theta_p=2 while for d<4 its value is increased to
first order in epsilon = 4-d. Combining a method developed by Majumdar and Sire
with renormalization group techniques we compute the correction to theta_p to
first order in epsilon. The global persistence exponent is found to be a new
and independent exponent. We finally compare our results with existing
simulations.Comment: 15 pages, LaTeX, one .eps figure include
Levy-flight spreading of epidemic processes leading to percolating clusters
We consider two stochastic processes, the Gribov process and the general
epidemic process, that describe the spreading of an infectious disease. In
contrast to the usually assumed case of short-range infections that lead, at
the critical point, to directed and isotropic percolation respectively, we
consider long-range infections with a probability distribution decaying in d
dimensions with the distance as 1/R^{d+\sigma}. By means of Wilson's momentum
shell renormalization-group recursion relations, the critical exponents
characterizing the growing fractal clusters are calculated to first order in an
\epsilon-expansion. It is shown that the long-range critical behavior changes
continuously to its short-range counterpart for a decay exponent of the
infection \sigma =\sigma_c>2.Comment: 9 pages ReVTeX, 2 postscript figures included, submitted to Eur.
Phys. J.
Microscopic Non-Universality versus Macroscopic Universality in Algorithms for Critical Dynamics
We study relaxation processes in spin systems near criticality after a quench
from a high-temperature initial state. Special attention is paid to the stage
where universal behavior, with increasing order parameter emerges from an early
non-universal period. We compare various algorithms, lattice types, and
updating schemes and find in each case the same universal behavior at
macroscopic times, despite of surprising differences during the early
non-universal stages.Comment: 9 pages, 3 figures, RevTeX, submitted to Phys. Rev. Let
Generalized Dynamic Scaling for Critical Relaxations
The dynamic relaxation process for the two dimensional Potts model at
criticality starting from an initial state with very high temperature and
arbitrary magnetization is investigated with Monte Carlo methods. The results
show that there exists universal scaling behaviour even in the short-time
regime of the dynamic evolution. In order to describe the dependence of the
scaling behaviour on the initial magnetization, a critical characteristic
function is introduced.Comment: Latex, 8 pages, 3 figures, to appear in Phys. Rev. Let
Non-Markovian Persistence and Nonequilibrium Critical Dynamics
The persistence exponent \theta for the global order parameter, M(t), of a
system quenched from the disordered phase to its critical point describes the
probability, p(t) \sim t^{-\theta}, that M(t) does not change sign in the time
interval t following the quench. We calculate \theta to O(\epsilon^2) for model
A of critical dynamics (and to order \epsilon for model C) and show that at
this order M(t) is a non-Markov process. Consequently, \theta is a new
exponent. The calculation is performed by expanding around a Markov process,
using a simplified version of the perturbation theory recently introduced by
Majumdar and Sire [Phys. Rev. Lett. _77_, 1420 (1996); cond-mat/9604151].Comment: 4 pages, Revtex, no figures, requires multicol.st
Generalized Dynamic Scaling for Critical Magnetic Systems
The short-time behaviour of the critical dynamics for magnetic systems is
investigated with Monte Carlo methods. Without losing the generality, we
consider the relaxation process for the two dimensional Ising and Potts model
starting from an initial state with very high temperature and arbitrary
magnetization. We confirm the generalized scaling form and observe that the
critical characteristic functions of the initial magnetization for the Ising
and the Potts model are quite different.Comment: 32 pages with15 eps-figure
Monte Carlo Simulations of Short-time Critical Dynamics with a Conserved Quantity
With Monte Carlo simulations, we investigate short-time critical dynamics of
the three-dimensional anti-ferromagnetic Ising model with a globally conserved
magnetization (not the order parameter). From the power law behavior of
the staggered magnetization (the order parameter), its second moment and the
auto-correlation, we determine all static and dynamic critical exponents as
well as the critical temperature. The universality class of is the same
as that without a conserved quantity, but the universality class of non-zero
is different.Comment: to appear in Phys. Rev.
Finite Size Scaling and Critical Exponents in Critical Relaxation
We simulate the critical relaxation process of the two-dimensional Ising
model with the initial state both completely disordered or completely ordered.
Results of a new method to measure both the dynamic and static critical
exponents are reported, based on the finite size scaling for the dynamics at
the early time. From the time-dependent Binder cumulant, the dynamical exponent
is extracted independently, while the static exponents and
are obtained from the time evolution of the magnetization and its higher
moments.Comment: 24 pages, LaTeX, 10 figure
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