744 research outputs found
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
Pair contact process with diffusion - A new type of nonequilibrium critical behavior?
Recently Carlon et. al. investigated the critical behavior of the pair
contact process with diffusion [cond-mat/9912347]. Using density matrix
renormalization group methods, they estimate the critical exponents, raising
the possibility that the transition might belong to the same universality class
as branching annihilating random walks with even numbers of offspring. This is
surprising since the model does not have an explicit parity-conserving
symmetry. In order to understand this contradiction, we estimate the critical
exponents by Monte Carlo simulations. The results suggest that the transition
might belong to a different universality class that has not been investigated
before.Comment: RevTeX, 3 pages, 2 eps figures, adapted to final version of
cond-mat/991234
Epidemic processes with immunization
We study a model of directed percolation (DP) with immunization, i.e. with
different probabilities for the first infection and subsequent infections. The
immunization effect leads to an additional non-Markovian term in the
corresponding field theoretical action. We consider immunization as a small
perturbation around the DP fixed point in d<6, where the non-Markovian term is
relevant. The immunization causes the system to be driven away from the
neighbourhood of the DP critical point. In order to investigate the dynamical
critical behaviour of the model, we consider the limits of low and high first
infection rate, while the second infection rate remains constant at the DP
critical value. Scaling arguments are applied to obtain an expression for the
survival probability in both limits. The corresponding exponents are written in
terms of the critical exponents for ordinary DP and DP with a wall. We find
that the survival probability does not obey a power law behaviour, decaying
instead as a stretched exponential in the low first infection probability limit
and to a constant in the high first infection probability limit. The
theoretical predictions are confirmed by optimized numerical simulations in 1+1
dimensions.Comment: 12 pages, 11 figures. v.2: minor correction
Differences between regular and random order of updates in damage spreading simulations
We investigate the spreading of damage in the three-dimensional Ising model
by means of large-scale Monte-Carlo simulations. Within the Glauber dynamics we
use different rules for the order in which the sites are updated. We find that
the stationary damage values and the spreading temperature are different for
different update order. In particular, random update order leads to larger
damage and a lower spreading temperature than regular order. Consequently,
damage spreading in the Ising model is non-universal not only with respect to
different update algorithms (e.g. Glauber vs. heat-bath dynamics) as already
known, but even with respect to the order of sites.Comment: final version as published, 4 pages REVTeX, 2 eps figures include
Phase diagram of a probabilistic cellular automaton with three-site interactions
We study a (1+1) dimensional probabilistic cellular automaton that is closely
related to the Domany-Kinzel (DKCA), but in which the update of a given site
depends on the state of {\it three} sites at the previous time step. Thus,
compared with the DKCA, there is an additional parameter, , representing
the probability for a site to be active at time , given that its nearest
neighbors and itself were active at time . We study phase transitions and
critical behavior for the activity {\it and} for damage spreading, using one-
and two-site mean-field approximations, and simulations, for and
. We find evidence for a line of tricritical points in the () parameter space, obtained using a mean-field approximation at pair level.
To construct the phase diagram in simulations we employ the growth-exponent
method in an interface representation. For , the phase diagram is
similar to the DKCA, but the damage spreading transition exhibits a reentrant
phase. For , the growth-exponent method reproduces the two absorbing
states, first and second-order phase transitions, bicritical point, and damage
spreading transition recently identified by Bagnoli {\it et al.} [Phys. Rev.
E{\bf 63}, 046116 (2001)].Comment: 15 pages, 7 figures, submited to PR
Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below
In order to check on a recent suggestion that local scale invariance
[M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the
dynamics is of Gaussian nature, we have carried out the measurement of the
response function in the kinetic Ising model with Glauber dynamics quenched to
in , where Gaussian behavior is expected to apply, and in the two
other cases of the model quenched to and to below , where
instead deviations from Gaussian behavior are expected to appear. We find that
in the case there is an excellent agreement between the numerical data,
the local scale invariance prediction and the analytical Gaussian
approximation. No logarithmic corrections are numerically detected. Conversely,
in the cases, both in the quench to and to below , sizable
deviations of the local scale invariance behavior from the numerical data are
observed. These results do support the idea that local scale invariance might
miss to capture the non Gaussian features of the dynamics. The considerable
precision needed for the comparison has been achieved through the use of a fast
new algorithm for the measurement of the response function without applying the
external field. From these high quality data we obtain for
the scaling exponent of the response function in the Ising model quenched
to below , in agreement with previous results.Comment: 24 pages, 6 figures. Resubmitted version with improved discussions
and figure
On Matrix Product States for Periodic Boundary Conditions
The possibility of a matrix product representation for eigenstates with
energy and momentum zero of a general m-state quantum spin Hamiltonian with
nearest neighbour interaction and periodic boundary condition is considered.
The quadratic algebra used for this representation is generated by 2m operators
which fulfil m^2 quadratic relations and is endowed with a trace. It is shown
that {\em not} every eigenstate with energy and momentum zero can be written as
matrix product state. An explicit counter-example is given. This is in contrast
to the case of open boundary conditions where every zero energy eigenstate can
be written as a matrix product state using a Fock-like representation of the
same quadratic algebra.Comment: 7 pages, late
Absorbing boundaries in the conserved Manna model
The conserved Manna model with a planar absorbing boundary is studied in
various space dimensions. We present a heuristic argument that allows one to
compute the surface critical exponent in one dimension analytically. Moreover,
we discuss the mean field limit that is expected to be valid in d>4 space
dimensions and demonstrate how the corresponding partial differential equations
can be solved.Comment: 8 pages, 4 figures; v1 was changed by replacing the co-authors name
"L\"ubeck" with "Lubeck" (metadata only
From multiplicative noise to directed percolation in wetting transitions
A simple one-dimensional microscopic model of the depinning transition of an
interface from an attractive hard wall is introduced and investigated. Upon
varying a control parameter, the critical behaviour observed along the
transition line changes from a directed-percolation to a multiplicative-noise
type. Numerical simulations allow for a quantitative study of the multicritical
point separating the two regions, Mean-field arguments and the mapping on a yet
simpler model provide some further insight on the overall scenario.Comment: 4 pages, 3 figure
Entanglement versus mutual information in quantum spin chains
The quantum entanglement of a bipartite quantum Ising chain is compared
with the mutual information between the two parts after a local measurement
of the classical spin configuration. As the model is conformally invariant, the
entanglement measured in its ground state at the critical point is known to
obey a certain scaling form. Surprisingly, the mutual information of classical
spin configurations is found to obey the same scaling form, although with a
different prefactor. Moreover, we find that mutual information and the
entanglement obey the inequality in the ground state as well as in a
dynamically evolving situation. This inequality holds for general bipartite
systems in a pure state and can be proven using similar techniques as for
Holevo's bound.Comment: 10 pages, 3 figure
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