97 research outputs found
Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics
In this paper we investigate the relation between the scaling properties of
the linear response function , of the thermoremanent magnetization
(TRM) and of the zero field cooled magnetization (ZFC) in the context of phase
ordering kinetics. We explain why the retrival of the scaling properties of
from those of TRM and ZFC is not trivial. Preasymptotic contributions
generate a long crossover in TRM, while ZFC is affected by a dangerous
irrelevant variable. Lack of understanding of both these points has generated
some confusion in the literature. The full picture relating the exponents of
all the quantities involved is explicitely illustrated in the framework of the
large model. Following this scheme, an assessment of the present status of
numerical simulations for the Ising model can be made. We reach the conclusion
that on the basis of the data available up to now, statements on the scaling
properties of can be made from ZFC but not from TRM. From ZFC data for
the Ising model with we confirm the previously found linear
dependence on dimensionality of the exponent entering . We also find evidence that a recently derived form of the
scaling function , using local scale invariance arguments [M.Henkel,
M.Pleimling, C.Godr\`{e}che and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701
(2001)], does not hold for the Ising model.Comment: 26 pages, 14 figure
Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets
We discuss the interplay between the degree of dynamical stochasticity,
memory persistence and violation of the self-averaging property in the aging
kinetics of quenched ferromagnets. We show that, in general, the longest
possible memory effects, which correspond to the slowest possible temporal
decay of the correlation function, are accompanied by the largest possible
violation of self-averaging and a quasi-deterministic descent into the ergodic
components. This phenomenon is observed in different systems, such as the Ising
model with long-range interactions, including mean-field, and the short-range
random field Ising model.Comment: Introduction strongly revised, changed figures. Accepted for
publication as a Rapid Communication in Physical Review
Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
We derive for Ising spins an off-equilibrium generalization of the
fluctuation dissipation theorem, which is formally identical to the one
previously obtained for soft spins with Langevin dynamics [L.F.Cugliandolo,
J.Kurchan and G.Parisi, J.Phys.I France \textbf{4}, 1641 (1994)]. The result is
quite general and holds both for dynamics with conserved and non conserved
order parameter. On the basis of this fluctuation dissipation relation, we
construct an efficient numerical algorithm for the computation of the linear
response function without imposing the perturbing field, which is alternative
to those of Chatelain [J.Phys. A \textbf{36}, 10739 (2003)] and Ricci-Tersenghi
[Phys.Rev.E {\bf 68}, 065104(R) (2003)]. As applications of the new algorithm,
we present very accurate data for the linear response function of the Ising
chain, with conserved and non conserved order parameter dynamics, finding that
in both cases the structure is the same with a very simple physical
interpretation. We also compute the integrated response function of the two
dimensional Ising model, confirming that it obeys scaling , with , as previously found with a different
method.Comment: 12 pages, 5 figure
Phase ordering in 3d disordered systems
We study numerically the phase-ordering kinetics of the site-diluted and
bond-diluted Ising models after a quench from an infinite to a low temperature.
We show that the speed of growth of the ordered domain's size is non-monotonous
with respect to the amount of dilution : Starting from the pure case
the system slows down when dilution is added, as it is usually expected when
disorder is introduced, but only up to a certain value beyond which the
speed of growth raises again. We interpret this counterintuitive fact in a
renormalization-group inspired framework, along the same lines proposed for the
corresponding two-dimensional systems, where a similar pattern was observed.Comment: 8 pages, 4 figures.To appear on Journal of Statistical Mechanics:
Theory and Experiment. arXiv admin note: text overlap with arXiv:1306.514
On a relation between roughening and coarsening
We argue that a strict relation exists between two in principle unrelated
quantities: The size of the growing domains in a coarsening system, and the
kinetic roughening of an interface. This relation is confirmed by extensive
simulations of the Ising model with different forms of quenched disorder, such
as random bonds, random fields and stochastic dilution.Comment: 8 pages, 3 figures. To appear on EP
Roughening of an interface in a system with surface or bulk disorder
We study numerically the roughening properties of an interface in a
two-dimensional Ising model with either random bonds or random fields, which
are representative of universality classes where disorder acts only on the
interface or also away from it, in the bulk. The dynamical structure factor
shows a rich crossover pattern from the form of a pure system at large
wavevectors , to a different behavior, typical of the kind of disorder, at
smaller 's. For the random field model a second crossover is observed from
the typical behavior of a system where disorder is only effective on the
surface, as the random bond model, to the truly large scale behavior, where
bulk-disorder is important, that is observed at the smallest wavevectors.Comment: 13 pages, 8 figure
Comment on "Scaling of the linear response in simple aging systems without disorder"
We have repeated the simulations of Henkel, Paessens and Pleimling (HPP)
[Phys.Rev.E {\bf 69}, 056109 (2004)] for the field-cooled susceptibility
in the quench of ferromagnetic systems to
and below . We show that, contrary to the statement made by HPP, the
exponent coincides with the exponent of the linear response function
. We point out what are the assumptions in the
argument of HPP that lead them to the conclusion .Comment: 4 pages, 4 figure
Dynamical scaling in branching models for seismicity
We propose a branching process based on a dynamical scaling hypothesis
relating time and mass. In the context of earthquake occurrence, we show that
experimental power laws in size and time distribution naturally originate
solely from this scaling hypothesis. We present a numerical protocol able to
generate a synthetic catalog with an arbitrary large number of events. The
numerical data reproduce the hierarchical organization in time and magnitude of
experimental inter-event time distribution.Comment: 3 figures to appear on Physical Review Letter
Fluctuation-dissipation relations and field-free algorithms for the computation of response functions
We discuss the relation between the fluctuation-dissipation relation derived
by Chatelain and Ricci-Tersenghi [C.Chatelain, J.Phys. A {\bf 36}, 10739
(2003); F. Ricci-Tersenghi, Phys.Rev.E 68, 065104(R) (2003)] and that by
Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi and M. Zannetti Phys. Rev.
E {\bf 72}, 056103 (2005)]. In order to do that, we re-derive the
fluctuation-dissipation relation for systems of discrete variables evolving in
discrete time via a stochastic non-equilibrium Markov process. The calculation
is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi
result and that by Lippiello-Corberi-Zannetti as special cases. The
applicability, generality, and experimental feasibility of the two approaches
is thoroughly discussed. Extending the analytical calculation to the variance
of the response function we show the vantage of field-free numerical methods
with respect to the standard method where the perturbation is applied. We also
show that the signal to noise ratio is better (by a factor ) in the
algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci
Tersenghi.Comment: 17 pages, 5 figures. To appear in Phys. Rev.
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