42 research outputs found
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
Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics
Using a representation of the q-deformed Lorentz algebra as differential
operators on quantum Minkowski space, we define an algebra of observables for a
q-deformed relativistic quantum mechanics with spin zero. We construct a
Hilbert space representation of this algebra in which the square of the mass is diagonal.Comment: 13 pages, LMU-TPW 94-
Scaling of the linear response in simple ageing systems without disorder
The time-dependent scaling of the thermoremanent and zero-field-cooled
susceptiblities in ferromagnetic spin systems undergoing ageing after a quench
to a temperature at or below criticality is studied. A recent debate on their
interpretation is resolved by showing that for systems with a short-ranged
equilibrium spin-spin correlator and above their roughening temperature, the
field-cooled susceptibility where
is related to the equilibrium magnetization and the exponent A is related to
the time-dependent scaling of the interface width between ordered domains. The
same effect also dominates the scaling of the zero-field-cooled susceptibility
, but does not enter into the thermoremanent
susceptibility . However, there may be large finite-time
corrections to the scaling of which are explicitly
derived and may be needed in order to extract reliable ageing exponents.
Consistency with the predictions of local scale invariance is confirmed in the
Glauber-Ising and spherical models.Comment: Latex2e, 14 pages, with 6 figure
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
Is local scale invariance a generic property of ageing phenomena ?
In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J.
Phys. A 37, 10479] it is shown that the critical autoresponse function of the
1+1-dimensional contact process is not in agreement with the predictions of
local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques
Dynamics of dilute disordered models: a solvable case
We study the dynamics of a dilute spherical model with two body interactions
and random exchanges. We analyze the Langevin equations and we introduce a
functional variational method to study generic dilute disordered models. A
crossover temperature replaces the dynamic transition of the fully-connected
limit. There are two asymptotic regimes, one determined by the central band of
the spectral density of the interactions and a slower one determined by
localized configurations on sites with high connectivity. We confront the
behavior of this model to the one of real glasses.Comment: 7 pages, 4 figures. Clarified, final versio
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
Superuniversality in phase-ordering disordered ferromagnets
The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model
with uniform bond disorder is investigated by intensive Monte Carlo
simulations. Simple ageing behaviour is observed in the single-time correlator
and the two-time responses and correlators. The dynamical exponent z and the
autocorrelation exponent lambda_C only depend on the ratio eps/T, where eps
describes the width of the distribution of the disorder, whereas a more
complicated behaviour is found for the non-equilibrium exponent a of the
two-time response as well as for the autoresponse exponent lambda_R. The
scaling functions are observed to depend only on the dimensionless ratio eps/T.
If the length scales are measured in terms of the time-dependent domain size
L(t), the form of the scaling functions is in general independent of both eps
and T. Conditions limiting the validity of this `superuniversality' are
discussed.Comment: Latex2e, 10pp with 8 figures included, PR macro
Irreversible spherical model and its stationary entropy production rate
The nonequilibrium stationary state of an irreversible spherical model is
investigated on hypercubic lattices. The model is defined by Langevin equations
similar to the reversible case, but with asymmetric transition rates. In spite
of being irreversible, we have succeeded in finding an explicit form for the
stationary probability distribution, which turns out to be of the
Boltzmann-Gibbs type. This enables one to evaluate the exact form of the
entropy production rate at the stationary state, which is non-zero if the
dynamical rules of the transition rates are asymmetric
Crossover from stationary to aging regime in glassy dynamics
We study the non-equilibrium dynamics of the spherical p-spin models in the
scaling regime near the plateau and derive the corresponding scaling functions
for the correlators. Our main result is that the matching between different
time regimes fixes the aging function in the aging regime to
. The exponent is related to the one giving the
length of the plateau. Interestingly is quickly very small when one
goes away from the dynamic transition temperature in the glassy phase. This
gives new light on the interpretation of experiments and simulations where
simple aging was found to be a reasonable but not perfect approximation, which
could be attributed to the existence of a small but non-zero stretching
exponent.Comment: 7 pages+2 figure