59 research outputs found
Equal-time correlation function for directed percolation
We suggest an equal-time n-point correlation function for systems in the
directed percolation universality class which is well defined in all phases and
independent of initial conditions. It is defined as the probability that all
points are connected with a common ancestor in the past by directed paths.Comment: LaTeX, 12 pages, 8 eps figure
On the predictive power of Local Scale Invariance
Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena
designed in the spirit of conformal invariance. For a given representation of
its generators it makes non-trivial predictions about the form of universal
scaling functions. In the past decade several representations have been
identified and the corresponding predictions were confirmed for various
anisotropic critical systems. Such tests are usually based on a comparison of
two-point quantities such as autocorrelation and response functions. The
present work highlights a potential problem of the theory in the sense that it
may predict any type of two-point function. More specifically, it is argued
that for a given two-point correlator it is possible to construct a
representation of the generators which exactly reproduces this particular
correlator. This observation calls for a critical examination of the predictive
content of the theory.Comment: 17 pages, 2 eps figure
Binary spreading process with parity conservation
Recently there has been a debate concerning the universal properties of the
phase transition in the pair contact process with diffusion (PCPD) . Although some of the critical exponents seem to coincide with
those of the so-called parity-conserving universality class, it was suggested
that the PCPD might represent an independent class of phase transitions. This
point of view is motivated by the argument that the PCPD does not conserve
parity of the particle number. In the present work we pose the question what
happens if the parity conservation law is restored. To this end we consider the
the reaction-diffusion process . Surprisingly this
process displays the same type of critical behavior, leading to the conclusion
that the most important characteristics of the PCPD is the use of binary
reactions for spreading, regardless of whether parity is conserved or not.Comment: RevTex, 4pages, 4 eps figure
On the identification of quasiprimary scaling operators in local scale-invariance
The relationship between physical observables defined in lattice models and
the associated (quasi-)primary scaling operators of the underlying field-theory
is revisited. In the context of local scale-invariance, we argue that this
relationship is only defined up to a time-dependent amplitude and derive the
corresponding generalizations of predictions for two-time response and
correlation functions. Applications to non-equilibrium critical dynamics of
several systems, with a fully disordered initial state and vanishing initial
magnetization, including the Glauber-Ising model, the Frederikson-Andersen
model and the Ising spin glass are discussed. The critical contact process and
the parity-conserving non-equilibrium kinetic Ising model are also considered.Comment: 12 pages, Latex2e with IOP macros, 2 figures included; final for
Transfer-matrix DMRG for stochastic models: The Domany-Kinzel cellular automaton
We apply the transfer-matrix DMRG (TMRG) to a stochastic model, the
Domany-Kinzel cellular automaton, which exhibits a non-equilibrium phase
transition in the directed percolation universality class. Estimates for the
stochastic time evolution, phase boundaries and critical exponents can be
obtained with high precision. This is possible using only modest numerical
effort since the thermodynamic limit can be taken analytically in our approach.
We also point out further advantages of the TMRG over other numerical
approaches, such as classical DMRG or Monte-Carlo simulations.Comment: 9 pages, 9 figures, uses IOP styl
Directed percolation with a single defect site
In a recent study [arXiv:1011.3254] the contact process with a modified
creation rate at a single site was shown to exhibit a non-universal scaling
behavior with exponents varying with the creation rate at the special site. In
the present work we argue that the survival probability decays according to a
stretched exponential rather than a power law, explaining previous
observations.Comment: 8 pages, 3 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
Phase transition of the one-dimensional coagulation-production process
Recently an exact solution has been found (M.Henkel and H.Hinrichsen,
cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A
with equal diffusion and coagulation rates. This model evolves into the
inactive phase independently of the production rate with density
decay law. Here I show that cluster mean-field approximations and Monte Carlo
simulations predict a continuous phase transition for higher
diffusion/coagulation rates as considered in cond-mat/0010062. Numerical
evidence is given that the phase transition universality agrees with that of
the annihilation-fission model with low diffusions.Comment: 4 pages, 4 figures include
Ageing in disordered magnets and local scale-invariance
The ageing of the bond-disordered two-dimensional Ising model quenched to
below its critical point is studied through the two-time autocorrelator and
thermoremanent magnetization (TRM). The corresponding ageing exponents are
determined. The form of the scaling function of the TRM is well described by
the theory of local scale-invariance.Comment: Latex2e, with epl macros, 7 pages, final for
Phase transition of a two dimensional binary spreading model
We investigated the phase transition behavior of a binary spreading process
in two dimensions for different particle diffusion strengths (). We found
that cluster mean-field approximations must be considered to get
consistent singular behavior. The approximations result in a continuous
phase transition belonging to a single universality class along the phase transition line. Large scale simulations of the particle density
confirmed mean-field scaling behavior with logarithmic corrections. This is
interpreted as numerical evidence supporting that the upper critical dimension
in this model is .The pair density scales in a similar way but with an
additional logarithmic factor to the order parameter. At the D=0 endpoint of
the transition line we found DP criticality.Comment: 8 pages, 10 figure
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