39 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
Kinetics of the long-range spherical model
The kinetic spherical model with long-range interactions is studied after a
quench to or to . For the two-time response and correlation
functions of the order-parameter as well as for composite fields such as the
energy density, the ageing exponents and the corresponding scaling functions
are derived. The results are compared to the predictions which follow from
local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo
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
Ageing, dynamical scaling and its extensions in many-particle systems without detailed balance
Recent studies on the phenomenology of ageing in certain many-particle
systems which are at a critical point of their non-equilibrium steady-states,
are reviewed. Examples include the contact process, the parity-conserving
branching-annihilating random walk, two exactly solvable particle-reaction
models and kinetic growth models. While the generic scaling descriptions known
from magnetic system can be taken over, some of the scaling relations between
the ageing exponents are no longer valid. In particular, there is no obvious
generalization of the universal limit fluctuation-dissipation ratio. The form
of the scaling function of the two-time response function is compared with the
prediction of the theory of local scale-invariance.Comment: Latex2e with IOP macros, 32 pages; extended discussion on contact
process and new section on kinetic growth processe
Ageing in bosonic particle-reaction models with long-range transport
Ageing in systems without detailed balance is studied in bosonic contact and
pair-contact processes with Levy diffusion. In the ageing regime, the dynamical
scaling of the two-time correlation function and two-time response function is
found and analysed. Exact results for non-equilibrium exponents and scaling
functions are derived. The behaviour of the fluctuation-dissipation ratio is
analysed. A passage time from the quasi-stationary regime to the ageing regime
is defined, in qualitative agreement with kinetic spherical models and p-spin
spherical glasses.Comment: Latex2e, 24 pages, with 9 figures include
Ageing without detailed balance: local scale invariance applied to two exactly solvable models
I consider ageing behaviour in two exactly solvable reaction-diffusion
systems. Ageing exponents and scaling functions are determined. I discuss in
particular a case in which the equality of two critical exponents, known from
systems with detailed balance, does not hold any more. Secondly it is shown
that the form of the scaling functions can be understood by symmetry
considerations.Comment: 6 pages, contribution to the summer school "Ageing and the Glass
Transition" held in Luxemburg in September 05. Published versio
Exact two-time correlation and response functions in the one-dimensional coagulation-diffusion process by the empty-interval-particle method
The one-dimensional coagulation-diffusion process describes the strongly
fluctuating dynamics of particles, freely hopping between the nearest-neighbour
sites of a chain such that one of them disappears with probability 1 if two
particles meet. The exact two-time correlation and response function in the
one-dimensional coagulation-diffusion process are derived from the
empty-interval-particle method. The main quantity is the conditional
probability of finding an empty interval of n consecutive sites, if at distance
d a site is occupied by a particle. Closed equations of motion are derived such
that the probabilities needed for the calculation of correlators and responses,
respectively, are distinguished by different initial and boundary conditions.
In this way, the dynamical scaling of these two-time observables is analysed in
the longtime ageing regime. A new generalised fluctuation-dissipation ratio
with an universal and finite limit is proposed.Comment: 31 pages, submitted to J.Stat.Mec
The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance
Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling,
J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo
simulations the linear response function of the two-dimensional Ising model
with Glauber dynamics quenched to the critical point. At variance with the
results of Henkel et al., we detect discrepancies between the actual scaling
behavior of the response function and the prediction of Local Scale Invariance.
Such differences are clearly visible in the impulse autoresponse function,
whereas they are drastically reduced in integrated response functions.
Accordingly, the scaling form predicted on the basis of Local Scale Invariance
simply provides an accurate fitting form for some quantities but cannot be
considered to be exact.Comment: 25 pages, 4 figure
Kinetics of phase-separation in the critical spherical model and local scale-invariance
The scaling forms of the space- and time-dependent two-time correlation and
response functions are calculated for the kinetic spherical model with a
conserved order-parameter and quenched to its critical point from a completely
disordered initial state. The stochastic Langevin equation can be split into a
noise part and into a deterministic part which has local scale-transformations
with a dynamical exponent z=4 as a dynamical symmetry. An exact reduction
formula allows to express any physical average in terms of averages calculable
from the deterministic part alone. The exact spherical model results are shown
to agree with these predictions of local scale-invariance. The results also
include kinetic growth with mass conservation as described by the
Mullins-Herring equation.Comment: Latex2e with IOP macros, 28 pp, 2 figures, final for
Ageing in the contact process: Scaling behavior and universal features
We investigate some aspects of the ageing behavior observed in the contact
process after a quench from its active phase to the critical point. In
particular we discuss the scaling properties of the two-time response function
and we calculate it and its universal ratio to the two-time correlation
function up to first order in the field-theoretical epsilon-expansion. The
scaling form of the response function does not fit the prediction of the theory
of local scale invariance. Our findings are in good qualitative agreement with
recent numerical results.Comment: 20 pages, 3 figure