14 research outputs found
Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance
The time-dependent scaling of the two-time autocorrelation function of spin
systems without disorder undergoing phase-ordering kinetics is considered. Its
form is shown to be determined by an extension of dynamical scaling to a local
scale-invariance which turns out to be a new version of conformal invariance.
The predicted autocorrelator is in agreement with Monte-Carlo data on the
autocorrelation function of the 2D kinetic Ising model with Glauber dynamics
quenched to a temperature below criticality.Comment: Latex2e, 7 pages with 2 figures, with epl macro, final from, to
appear in EP
Ageing in the critical contact process: a Monte Carlo study
The long-time dynamics of the critical contact process which is brought
suddenly out of an uncorrelated initial state undergoes ageing in close analogy
with quenched magnetic systems. In particular, we show through Monte Carlo
simulations in one and two dimensions and through mean-field theory that
time-translation invariance is broken and that dynamical scaling holds. We find
that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R
are equal but, in contrast to systems relaxing to equilibrium, the ageing
exponents a and b are distinct. A recent proposal to define a non-equilibrium
temperature through the short-time limit of the fluctuation-dissipation ratio
is therefore not applicable.Comment: 18 pages, 7 figures, Latex2e with IOP macros; final for
Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics
The scaling of the spatio-temporal response of coarsening systems is studied
through simulations of the 2D and 3D Ising model with Glauber dynamics. The
scaling functions agree with the prediction of local scale invariance,
extending dynamical scaling to a space-time dynamical symmetry.Comment: Latex, 4 pages, 4 figure
Ageing and dynamical scaling in the critical Ising spin glass
The non-equilibrium ageing behaviour of the 3D and 4D critical Ising spin
glass is studied for both binary and gaussian disorder. The same phenomenology
of the time-dependent scaling as in non-disordered magnets is found but the
non-equilibrium exponents and the universal limit fluctuation-dissipation ratio
depend on the distribution of the coupling constants.Comment: Latex2e, 7 pages with epl macro, 4 figures included, 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 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
On the scaling and ageing behaviour of the alternating susceptibility in spin glasses and local scale-invariance
The frequency-dependent scaling of the dispersive and dissipative parts of
the alternating susceptibility is studied for spin glasses at criticality. An
extension of the usual -scaling is proposed. Simulational data from
the three-dimensional Ising spin glass agree with this new scaling form and
moreover reproduce well the scaling functions explicitly calculated for systems
satisfying local scale-invariance. There is also a qualitative agreement with
existing experimental data.Comment: 19 pages, 2 figures, to appear in special issue of J. Phys. Cond.
Matt. dedicated to Lothar Schaefer on the occasion of his 60th birthday,
final form with IOP macro
Scaling of the magnetic linear response in phase-ordering kinetics
The scaling of the thermoremanent magnetization and of the dissipative part
of the non-equilibrium magnetic susceptibility is analysed as a function of the
waiting-time for a simple ferromagnet undergoing phase-ordering kinetics
after a quench into the ferromagnetically ordered phase. Their scaling forms
describe the cross-over between two power-law regimes governed by the
non-equilibrium exponents and , respectively. A relation
between , the dynamical exponent and the equilibrium exponent is
derived from scaling arguments. Explicit tests in the Glauber-Ising model and
the kinetic spherical model are presented.Comment: 7 pages, 2 figures included, needs epl.cls, version to appear in
Europhys. Let
Ageing phenomena without detailed balance: the contact process
The long-time dynamics of the 1D contact process suddenly brought out of an
uncorrelated initial state is studied through a light-cone transfer-matrix
renormalisation group approach. At criticality, the system undergoes ageing
which is characterised through the dynamical scaling of the two-times
autocorrelation and autoresponse functions. The observed non-equality of the
ageing exponents a and b excludes the possibility of a finite
fluctuation-dissipation ratio in the ageing regime. The scaling form of the
critical autoresponse function is in agreement with the prediction of local
scale-invariance.Comment: 20 pages, 15 figures, Latex2e with IOP macro
Out-of-equilibrium properties of the semi-infinite kinetic spherical model
We study the ageing properties of the semi-infinite kinetic spherical model
at the critical point and in the ordered low-temperature phase, both for
Dirichlet and Neumann boundary conditions. The surface fluctuation-dissipation
ratio and the scaling functions of two-time surface correlation and response
functions are determined explicitly in the dynamical scaling regime. In the
low-temperature phase our results show that for the case of Dirichlet boundary
conditions the value of the non-equilibrium surface exponent differs from
the usual bulk value of systems undergoing phase ordering.Comment: 22 pages, 4 figures included, submitted to J. Phys.