62 research outputs found
Reply to a Comment
Reply to the Comment by F. Corberi, E. Lipiello and M. Zannetti
(cond-mat/0211609)
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
Corrections to local scale invariance in the non-equilibrium dynamics of critical systems: numerical evidences
Local scale invariance (LSI) has been recently proposed as a possible
extension of the dynamical scaling in systems at the critical point and during
phase ordering. LSI has been applied inter alia to provide predictions for the
scaling properties of the response function of non-equilibrium critical systems
in the aging regime following a quench from the high-temperature phase to the
critical point. These predictions have been confirmed by Monte Carlo
simulations and analytical results for some specific models, but they are in
disagreement with field-theoretical predictions. By means of Monte Carlo
simulations of the critical two- and three-dimensional Ising model with Glauber
dynamics, we study the intermediate integrated response, finding deviations
from the corresponding LSI predictions that are in qualitative agreement with
the field-theoretical computations. This result casts some doubts on the
general applicability of LSI to critical dynamics.Comment: 4 pages, 2 figures, minor changes, version to appear in Phys. Rev. B
as a Rapid Communicatio
Ising cubes with enhanced surface couplings
Using Monte Carlo techniques, Ising cubes with ferromagnetic nearest-neighbor
interactions and enhanced couplings between surface spins are studied. In
particular, at the surface transition, the corner magnetization shows
non-universal, coupling-dependent critical behavior in the thermodynamic limit.
Results on the critical exponent of the corner magnetization are compared to
previous findings on two-dimensional Ising models with three intersecting
defect lines.Comment: 4 pages, 2 figures included, submitted to Phys. Rev.
Phenomenology of ageing in the Kardar-Parisi-Zhang equation
We study ageing during surface growth processes described by the
one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial
state, the systems undergo simple ageing in both correlators and linear
responses and its dynamical scaling is characterised by the ageing exponents
a=-1/3, b=-2/3, lambda_C=lambda_R=1 and z=3/2. The form of the autoresponse
scaling function is well described by the recently constructed logarithmic
extension of local scale-invariance.Comment: Latex2e, 5 pages, with 4 figures, 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
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
Aging phenomena in critical semi-infinite systems
Nonequilibrium surface autocorrelation and autoresponse functions are studied
numerically in semi-infinite critical systems in the dynamical scaling regime.
Dynamical critical behaviour is examined for a nonconserved order parameter in
semi-infinite two- and three-dimensional Ising models as well as in the
Hilhorst-van Leeuwen model. The latter model permits a systematic study of
surface aging phenomena, as the surface critical exponents change continuously
as function of a model parameter. The scaling behaviour of surface two-time
quantities is investigated and scaling functions are confronted with
predictions coming from the theory of local scale invariance. Furthermore,
surface fluctuation-dissipation ratios are computed and their asymptotic values
are shown to depend on the values of surface critical exponents.Comment: 12 pages, figures included, version to appear in Phys. Rev.
Relaxation and Glassy Dynamics in Disordered Type-II Superconductors
We study the non-equilibrium relaxation kinetics of interacting magnetic flux
lines in disordered type-II superconductors at low temperatures by means of a
three-dimensional elastic line model and Monte Carlo simulations. Investigating
the vortex density and height autocorrelation functions as well as the flux
line mean-square displacement, we observe the emergence of glassy dynamics,
caused by the competing effects of vortex pinning due to point defects and
long-range repulsive interactions between the flux lines. Our systematic
numerical study allows us to carefully disentangle the associated different
relaxation mechanisms, and to assess their relative impact on the kinetics of
vortex matter at low temperatures.Comment: 12 pages, 9 figure
- …