14 research outputs found
Nonequilibrium critical dynamics of the three-dimensional gauge glass
We study the non-equilibrium aging behavior of the gauge glass model in three
dimensions at the critical temperature. We perform Monte Carlo simulations with
a Metropolis update, and correlation and response functions are calculated for
different waiting times. We obtain a multiplicative aging scaling of the
correlation and response functions, calculating the aging exponent and the
nonequilibrium autocorrelation decay exponent . We also analyze
the fluctuation-dissipation relationship at the critical temperature, obtaining
the critical fluctuation-dissipation ratio . By comparing our results
with the aging scaling reported previously for a model of interacting flux
lines in the vortex glass regime, we found that the exponents for both models
are very different.Comment: 7 pages, 4 figures. Manuscript accpeted for publication in PR
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.
Scaling and universality in the aging kinetics of the two-dimensional clock model
We study numerically the aging dynamics of the two-dimensional p-state clock
model after a quench from an infinite temperature to the ferromagnetic phase or
to the Kosterlitz-Thouless phase. The system exhibits the general scaling
behavior characteristic of non-disordered coarsening systems. For quenches to
the ferromagnetic phase, the value of the dynamical exponents, suggests that
the model belongs to the Ising-type universality class. Specifically, for the
integrated response function , we find
consistent with the value found in the two-dimensional
Ising model.Comment: 16 pages, 14 figures (please contact the authors for figures
Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state
The universality class, even the order of the transition, of the
two-dimensional Ising model depends on the range and the symmetry of the
interactions (Onsager model, Baxter-Wu model, Turban model, etc.), but the
critical temperature is generally the same due to self-duality. Here we
consider a sudden change in the form of the interaction and study the
nonequilibrium critical dynamical properties of the nearest-neighbor model. The
relaxation of the magnetization and the decay of the autocorrelation function
are found to display a power law behavior with characteristic exponents that
depend on the universality class of the initial state.Comment: 6 pages, 5 figures, submitted to Phys. Rev.
Aging and effective temperatures near a critical point
The orientation fluctuations of the director of a liquid crystal(LC) are
measured after a quench near the Fr\'eedericksz transition, which is a second
order transition driven by an electric field. We report experimental evidence
that, because of the critical slowing down, the LC presents, after the quench,
several properties of an aging system, such as power law scaling versus time of
correlation and response functions. During this slow relaxation, a well defined
effective temperature, much larger than the heat bath temperature, can be
measured using the fluctuation dissipation relation.Comment: to be published in PR
Domain growth and aging scaling in coarsening disordered systems
Using extensive Monte Carlo simulations we study aging properties of two
disordered systems quenched below their critical point, namely the
two-dimensional random-bond Ising model and the three-dimensional
Edwards-Anderson Ising spin glass with a bimodal distribution of the coupling
constants. We study the two-times autocorrelation and space-time correlation
functions and show that in both systems a simple aging scenario prevails in
terms of the scaling variable , where is the time-dependent
correlation length, whereas is the waiting time and is the observation
time. The investigation of the space-time correlation function for the
random-bond Ising model allows us to address some issues related to
superuniversality.Comment: 8 pages, 9 figures, to appear in European Physical Journal
On universality in aging ferromagnets
This work is a contribution to the study of universality in
out-of-equilibrium lattice models undergoing a second-order phase transition at
equilibrium. The experimental protocol that we have chosen is the following:
the system is prepared in its high-temperature phase and then quenched at the
critical temperature . We investigated by mean of Monte Carlo simulations
two quantities that are believed to take universal values: the exponent
obtained from the decay of autocorrelation functions and the
asymptotic value of the fluctuation-dissipation ratio . This
protocol was applied to the Ising model, the 3-state clock model and the
4-state Potts model on square, triangular and honeycomb lattices and to the
Ashkin-Teller model at the point belonging at equilibrium to the 3-state Potts
model universality class and to a multispin Ising model and the Baxter-Wu model
both belonging to the 4-state Potts model universality class at equilibrium.Comment: 17 page
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
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
On the definition of a unique effective temperature for non-equilibrium critical systems
We consider the problem of the definition of an effective temperature via the
long-time limit of the fluctuation-dissipation ratio (FDR) after a quench from
the disordered state to the critical point of an O(N) model with dissipative
dynamics. The scaling forms of the response and correlation functions of a
generic observable are derived from the solutions of the corresponding
Renormalization Group equations. We show that within the Gaussian approximation
all the local observables have the same FDR, allowing for a definition of a
unique effective temperature. This is no longer the case when fluctuations are
taken into account beyond that approximation, as shown by a computation up to
the first order in the epsilon-expansion for two quadratic observables. This
implies that, contrarily to what often conjectured, a unique effective
temperature can not be defined for this class of models.Comment: 32 pages, 5 figures. Minor changes, published versio