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Marco Zannetti

Publications and source records attributed to Marco Zannetti.

At least 37 records · Page 2Linked to original sources
arXiv2007

Fluctuation-Dissipation relations far from Equilibrium

In this Article we review some recent progresses in the field of non-equilibrium linear response theory. We show how a generalization of the fluctuation-dissipation theorem can be derived for Markov processes, and discuss the Cugliandolo-Kurchan \cite{Cugliandolo93} fluctuation dissipation relation for aging systems and the theorem by Franz {\it et. al.} \cite{Franz98} relating static and dynamic properties. We than specialize the subject to phase-ordering systems examining the scaling properties of the linear response function and how these are determined by the behavior of topological defects. We discuss how the connection between statics and dynamics can be violated in these systems at the lower critical dimension or as due to stochastic instability.

cond-mat.stat-mech↗
arXiv2006

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 $χ(t,s)\simeq s^{-a_χ}f(t/s)$, we find $a_χ$ consistent with the value $a_χ=0.28$ found in the two-dimensional Ising model.

cond-mat.stat-mech↗
arXiv2006

Test of Local Scale Invariance from the direct measurement of the response function in the Ising model quenched to and to below $T_C$

In order to check on a recent suggestion that local scale invariance [M.Henkel et al. Phys.Rev.Lett. {\bf 87}, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to $T_C$ in $d=4$, where Gaussian behavior is expected to apply, and in the two other cases of the $d=2$ model quenched to $T_C$ and to below $T_C$, where instead deviations from Gaussian behavior are expected to appear. We find that in the $d=4$ case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the $d=2$ cases, both in the quench to $T_C$ and to below $T_C$, sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain $a=0.27 \pm 0.002$ for the scaling exponent of the response function in the $d=2$ Ising model quenched to below $T_C$, in agreement with previous results.

cond-mat.stat-mech↗
arXiv2005

Correction to scaling in the response function of the 2d kinetic Ising model

The aging part $R_{ag}(t,s)$ of the impulsive response function of the two dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing a new algorithm without the imposition of the external field. We find that the simple scaling form $R_{ag}(t,s)=s^{-(1+a)}f(t/s)$, which is usually believed to hold in the aging regime, is not obeyed. We analyse the data assuming the existence of a correction to scaling. We find $a=0.273 \pm 0.006$, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function $f(t/s)$ and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for $R_{ag}(t,s)$. This gives a satisfactory qualitative agreement with the numerical data for $R_{ag}(t,s)$ and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in $R_{ag}(t,s)$, making this quantity the most convenient for the study of the asymptotic scaling properties.

cond-mat.stat-mech↗
arXiv2005

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 $χ_{FC}(t) - χ_0 \sim t^{-A}$ in the quench of ferromagnetic systems to and below $T_C$. We show that, contrary to the statement made by HPP, the exponent $A$ coincides with the exponent $a$ of the linear response function $R(t,s) \sim s^{-(1+a)}f_R(t/s)$. We point out what are the assumptions in the argument of HPP that lead them to the conclusion $A<a$.

cond-mat.stat-mech↗
arXiv2005

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 $χ(t,t_w)\simeq t_w^{-a}f(t/t_w)$, with $a =0.26\pm 0.01$, as previously found with a different method.

cond-mat.stat-mech↗
arXiv2004

Effective temperature in the quench of coarsening systems to and below $T_C$

We overview the general scaling behavior of the effective temperature in the que nches of simple non disordered systems, like ferromagnets, to and below $T_C$. Emphasis is on the behavior as d imensionality is varied. Consequences on the shape of the asymptotic parametric representation are derived. In particu lar, this is always trivial in the critical quenches with $T_C>0$. We clarify that the quench to $T_C=0$ at the lower critical dimensionality $d_L$, cannot be regarded as a critical quench. Implications for the behavior of the exponent $a$ of the aging response function in the quenches below $T_C$ are developed.

cond-mat.stat-mech↗
arXiv2003

Generic features of the fluctuation dissipation relation in coarsening systems

The integrated response function in phase-ordering systems with scalar, vector, conserved and non conserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution $χ_{ag} (t,t_w)= t_w ^{-a_χ} \hat χ(t/t_w)$ we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of $a_χ$ in all cases considered. The primary result is that $a_χ$ vanishes continuously as $d$ approaches the lower critical dimensionality $d_L$. This implies that i) the existence of a non trivial fluctuation dissipation relation and ii) the failure of the connection between statics and dynamics are generic features of phase ordering at $d_L$.

cond-mat.stat-mech↗
arXiv2003

Non trivial behavior of the linear response function in phase ordering kinetics

Drawing from exact, approximate and numerical results an overview of the properties of the out of equilibrium response function in phase ordering kinetics is presented. Focusing on the zero field cooled magnetization, emphasis is on those features of this quantity which display non trivial behavior when relaxation proceeds by coarsening. Prominent among these is the dimensionality dependence of the scaling exponent $a_χ$ which leads to failure of the connection between static and dynamic properties at the lower dimensionality $d_L$, where $a_χ=0$. We also analyse the mean spherical model as an explicit example of a stochastic unstable system, for which the connection between statics and dynamics fails at all dimensionalities.

cond-mat.stat-mech↗
arXiv2003

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 $R(t,s)$, 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 $R(t,s)$ 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 $N$ 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 $R(t,s)$ can be made from ZFC but not from TRM. From ZFC data for the Ising model with $d=2,3,4$ we confirm the previously found linear dependence on dimensionality of the exponent $a$ entering $R(t,s) \sim s^{-(1+a)}f(t/s)$. We also find evidence that a recently derived form of the scaling function $f(x)$, using local scale invariance arguments [M.Henkel, M.Pleimling, C.Godrèche and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701 (2001)], does not hold for the Ising model.

cond-mat.stat-mech↗
arXiv2002

Correlation Functions and Fluctuation-Dissipation Relation in Driven Mixtures: an exactly solvable model

The dynamics of a binary system with non conserved order parameter under a plain shear flow with rate $γ$ is solved analytically in the large-N limit. A phase transition is observed at a critical temperature $T_c(γ)$. After a quench from a high temperature equilibrium state to a lower temperature $T$ a non-equilibrium stationary state is entered when $T>T_c(γ)$, while aging dynamics characterizes the phases with $T\leq T_c(γ)$. Two-time quantities are computed and the off-equilibrium generalization of the fluctuation-dissipation theorem is provided.

cond-mat.stat-mech↗
arXiv2002

Universality of the off-equilibrium response function in the kinetic Ising chain

The off-equilibrium response function $χ(t,t_w)$ and autocorrelation function $C(t,t_w)$ of an Ising chain with spin-exchange dynamics are studied numerically and compared with the same quantities in the case of spin-flip dynamics. It is found that, even though these quantities are separately different in the two cases, the parametric plot of $χ(t,t_w)$ versus $C(t,t_w)$ is the same. While this result could be expected in higher dimensionality, where $χ(C)$ is related to the equilibrium state, it is far from trivial in the one dimensional case where this relation does not hold. The origin of the universality of $χ(C)$ is traced back to the optimization of domains position with respect to the perturbing external field. This mechanism is investigated resorting to models with a single domain moving in a random environment.

cond-mat.stat-mech↗
arXiv2002

Slow relaxation in the large N model for phase ordering

The basic features of the slow relaxation phenomenology arising in phase ordering processes are obtained analytically in the large $N$ model through the exact separation of the order parameter into the sum of thermal and condensation components. The aging contribution in the response function $χ_{ag}(t,t_w)$ is found to obey a pattern of behavior, under variation of dimensionality, qualitatively similar to the one observed in Ising systems. There exists a critical dimensionality $(d=4)$ above which $χ_{ag}(t,t_w)$ is proportional to the defect density $ρ_D(t)$, while for $d<4$ it vanishes more slowly than $ρ_D(t)$ and at $d=2$ does not vanish. As in the Ising case, this behavior can be understood in terms of the dependence on dimensionality of the interplay between the defect density and the effective response associated to a single defect.

cond-mat.stat-mech↗
arXiv2001

On the connection between off-equilibrium response and statics in non disordered coarsening systems

The connection between the out of equilibrium linear response function and static properties established by Franz, Mezard, Parisi and Peliti for slowly relaxing systems is analyzed in the context of phase ordering processes. Separating the response in the bulk of domains from interface response, we find that in order for the connection to hold the interface contribution must be asymptotically negligible. How fast this happens depends on the competition between interface curvature and the perturbing external field in driving domain growth. This competition depends on space dimensionality and there exists a critical value $d_c=3$ below which the interface response becomes increasingly important eventually invalidating the connection between statics and dynamics as the limit $d=1$ is reached. This mechanism is analyzed numerically for the Ising model with $d$ ranging from 1 to 4 and analytically for a continuous spin model with arbitrary dimensionality.

cond-mat.stat-mech↗
arXiv2001

Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems

The relationship between statics and dynamics proposed by Franz, Mezard, Parisi and Peliti (FMPP) for slowly relaxing systems [Phys.Rev.Lett. {\bf 81}, 1758 (1998)] is investigated in the framework of non disordered coarsening systems. Separating the bulk from interface response we find that for statics to be retrievable from dynamics the interface contribution must be asymptotically negligible. How fast this happens depends on dimensionality. There exists a critical dimensionality above which the interface response vanishes like the interface density and below which it vanishes more slowly. At $d=1$ the interface response does not vanish leading to the violation of the FMPP scheme. This behavior is explained in terms of the competition between curvature driven and field driven interface motion.

cond-mat.stat-mech↗
arXiv1999

Preasymptotic multiscaling in the phase-ordering dynamics of the kinetic Ising model

The evolution of the structure factor is studied during the phase-ordering dynamics of the kinetic Ising model with conserved order parameter. A preasymptotic multiscaling regime is found as in the solution of the Cahn-Hilliard-Cook equation, revealing that the late stage of phase-ordering is always approached through a crossover from multiscaling to standard scaling, independently from the nature of the microscopic dynamics.

cond-mat.stat-mech↗
arXiv1998

Overall time evolution in phase-ordering kinetics

The phenomenology from the time of the quench to the asymptotic behavior in the phase-ordering kinetics of a system with conserved order parameter is investigated in the Bray-Humayun model and in the Cahn-Hilliard-Cook model. From the comparison of the structure factor in the two models the generic pattern of the overall time evolution, based on the sequence ``early linear - intermediate mean field - late asymptotic regime'' is extracted. It is found that the time duration of each of these regimes is strongly dependent on the wave vector and on the parameters of the quench, such as the amplitude of the initial fluctuations and the final equilibrium temperature. The rich and complex crossover phenomenology arising as these parameters are varied can be accounted for in a simple way through the structure of the solution of the Bray-Humayun model.

cond-mat.stat-mech↗