13,837 research outputs found
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
Persistence of Manifolds in Nonequilibrium Critical Dynamics
We study the persistence P(t) of the magnetization of a d' dimensional
manifold (i.e., the probability that the manifold magnetization does not flip
up to time t, starting from a random initial condition) in a d-dimensional spin
system at its critical point. We show analytically that there are three
distinct late time decay forms for P(t) : exponential, stretched exponential
and power law, depending on a single parameter \zeta=(D-2+\eta)/z where D=d-d'
and \eta, z are standard critical exponents. In particular, our theory predicts
that the persistence of a line magnetization decays as a power law in the d=2
Ising model at its critical point. For the d=3 critical Ising model, the
persistence of the plane magnetization decays as a power law, while that of a
line magnetization decays as a stretched exponential. Numerical results are
consistent with these analytical predictions.Comment: 4 pages revtex, 1 eps figure include
Effects of Turbulent Mixing on the Critical Behavior
Effects of strongly anisotropic turbulent mixing on the critical behavior are
studied by means of the renormalization group. Two models are considered: the
equilibrium model A, which describes purely relaxational dynamics of a
nonconserved scalar order parameter, and the Gribov model, which describes the
nonequilibrium phase transition between the absorbing and fluctuating states in
a reaction-diffusion system. The velocity is modelled by the d-dimensional
generalization of the random shear flow introduced by Avellaneda and Majda
within the context of passive scalar advection. Existence of new nonequilibrium
types of critical regimes (universality classes) is established.Comment: Talk given in the International Bogolyubov Conference "Problems of
Theoretical and Mathematical Physics" (Moscow-Dubna, 21-27 August 2009
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.
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
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
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
Multifractal properties of resistor diode percolation
Focusing on multifractal properties we investigate electric transport on
random resistor diode networks at the phase transition between the
non-percolating and the directed percolating phase. Building on first
principles such as symmetries and relevance we derive a field theoretic
Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of
the current distribution that are governed by a family of critical exponents
. We calculate the family to two-loop order in a
diagrammatic perturbation calculation augmented by renormalization group
methods.Comment: 21 pages, 5 figures, to appear in Phys. Rev.
Dynamics-dependent criticality in models with q absorbing states
We study a one-dimensional, nonequilibrium Potts-like model which has
symmetric absorbing states. For , as expected, the model belongs to the
parity conserving universality class. For the critical behaviour depends
on the dynamics of the model. Under a certain dynamics it remains generically
in the active phase, which is also the feature of some other models with three
absorbing states. However, a modified dynamics induces a parity conserving
phase transition. Relations with branching-annihilating random walk models are
discussed in order to explain such a behaviour.Comment: 5 pages, 5 eps figures included, Phys.Rev.E (accepted
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