133 research outputs found
Ageing Properties of Critical Systems
In the past few years systems with slow dynamics have attracted considerable
theoretical and experimental interest. Ageing phenomena are observed during
this ever-lasting non-equilibrium evolution. A simple instance of such a
behaviour is provided by the dynamics that takes place when a system is
quenched from its high-temperature phase to the critical point. The aim of this
review is to summarize the various numerical and analytical results that have
been recently obtained for this case. Particular emphasis is put to the
field-theoretical methods that can be used to provide analytical predictions
for the relevant dynamical quantities. Fluctuation-dissipation relations are
discussed and in particular the concept of fluctuation-dissipation ratio (FDR)
is reviewed, emphasizing its connection with the definition of a possible
effective temperature. The Renormalization-Group approach to critical dynamics
is summarized and the scaling forms of the time-dependent non-equilibrium
correlation and response functions of a generic observable are discussed. From
them the universality of the associated FDR follows as an amplitude ratio. It
is then possible to provide predictions for ageing quantities in a variety of
different models. In particular the results for Model A, B, and C dynamics of
the O(N) Ginzburg-Landau Hamiltonian, and Model A dynamics of the weakly dilute
Ising magnet and of a \phi^3 theory, are reviewed and compared with the
available numerical results and exact solutions. The effect of a planar surface
on the ageing behaviour of Model A dynamics is also addressed within the
mean-field approximation.Comment: rvised enlarged version, 72 Pages, Topical Review accepted for
publication on JP
Aging and fluctuation-dissipation ratio for the diluted Ising Model
We consider the out-of-equilibrium, purely relaxational dynamics of a weakly
diluted Ising model in the aging regime at criticality. We derive at first
order in a expansion the two-time response and correlation
functions for vanishing momenta. The long-time limit of the critical
fluctuation-dissipation ratio is computed at the same order in perturbation
theory.Comment: 4 pages, 2 figure
Two-loop Critical Fluctuation-Dissipation Ratio for the Relaxational Dynamics of the O(N) Landau-Ginzburg Hamiltonian
The off-equilibrium purely dissipative dynamics (Model A) of the O(N) vector
model is considered at criticality in an up to
O(). The scaling behavior of two-time response and correlation
functions at zero momentum, the associated universal scaling functions, and the
nontrivial limit of the fluctuation-dissipation ratio are determined in the
aging regime.Comment: 21 pages, 6 figures. Discussion enlarged and two figures added. Final
version accepted for publication in Phys. Rev.
Colloidal aggregation and critical Casimir forces
A recent Letter [Phys. Rev. Lett. 103, 156101 (2009)] reports the
experimental observation of aggregation of colloidal particles dispersed in a
liquid mixture of heavy water and 3-methylpyridine. The experimental data are
interpreted in terms of a model which accounts solely for the competing effects
of the interparticle electrostatic repulsion and of the attractive critical
Casimir force. Here we show, however, that the reported aggregation actually
occurs within ranges of values of the correlation length and of the Debye
screening length ruled out by the proposed model and that a significant part of
the experimental data presented in the Letter cannot be consistently
interpreted in terms of such a model.Comment: 1 page, 1 figure; For the reply see arXiv:1007.077
Finite-Size Scaling in the Driven Lattice Gas
We present a Monte Carlo study of the high-temperature phase of the
two-dimensional driven lattice gas at infinite driving field. We define a
finite-volume correlation length, verify that this definition has a good
infinite-volume limit independent of the lattice geometry, and study its
finite-size-scaling behavior. The results for the correlation length are in
good agreement with the predictions based on the field theory proposed by
Janssen, Schmittmann, Leung, and Cardy. The theoretical predictions for the
susceptibility and the magnetization are also well verified. We show that the
transverse Binder parameter vanishes at the critical point in all dimensions
and discuss how such result should be expected in the theory of
Janssen et al. in spite of the existence of a dangerously irrelevant operator.
Our results confirm the Gaussian nature of the transverse excitations.Comment: 40 pages, in honour of G. Jona-Lasini
Dynamic crossover in the persistence probability of manifolds at criticality
We investigate the persistence properties of critical d-dimensional systems
relaxing from an initial state with non-vanishing order parameter (e.g., the
magnetization in the Ising model), focusing on the dynamics of the global order
parameter of a d'-dimensional manifold. The persistence probability P(t) shows
three distinct long-time decays depending on the value of the parameter \zeta =
(D-2+\eta)/z which also controls the relaxation of the persistence probability
in the case of a disordered initial state (vanishing order parameter) as a
function of the codimension D = d-d' and of the critical exponents z and \eta.
We find that the asymptotic behavior of P(t) is exponential for \zeta > 1,
stretched exponential for 0 <= \zeta <= 1, and algebraic for \zeta < 0. Whereas
the exponential and stretched exponential relaxations are not affected by the
initial value of the order parameter, we predict and observe a crossover
between two different power-law decays when the algebraic relaxation occurs, as
in the case d'=d of the global order parameter. We confirm via Monte Carlo
simulations our analytical predictions by studying the magnetization of a line
and of a plane of the two- and three-dimensional Ising model, respectively,
with Glauber dynamics. The measured exponents of the ultimate algebraic decays
are in a rather good agreement with our analytical predictions for the Ising
universality class. In spite of this agreement, the expected scaling behavior
of the persistence probability as a function of time and of the initial value
of the order parameter remains problematic. In this context, the
non-equilibrium dynamics of the O(n) model in the limit n->\infty and its
subtle connection with the spherical model is also discussed in detail.Comment: 23 pages, 6 figures; minor changes, added one figure, (old) fig.4
replaced by the correct fig.
Electrostatic interactions in critical solvents
The subtle interplay between critical phenomena and electrostatics is
investigated by considering the effective force acting on two parallel walls
confining a near-critical binary liquid mixture with added salt. The
ion-solvent coupling can turn a non-critical repulsive electrostatic force into
an attractive one upon approaching the critical point. However, the effective
force is eventually dominated by the critical Casimir effect, the universal
properties of which are not altered by the presence of salt. This observation
allows a consistent interpretation of recent experimental data.Comment: Submitte
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