arXiv subjects

Federico Corberi

Publications and source records attributed to Federico Corberi.

At least 73 records · Page 4Linked to original sources

arXiv2011

Heat exchanges in coarsening systems

This paper is a contribution to the understanding of the thermal properties of aging systems where statistically independent degrees of freedom with largely separated timescales are expected to coexist. Focusing on the prototypical case of quenched ferromagnets, where fast and slow modes can be respectively associated to fluctuations in the bulk of the coarsening domains and to their interfaces, we perform a set of numerical experiments specifically designed to compute the heat exchanges between different degrees of freedom. Our studies promote a scenario with fast modes acting as an equilibrium reservoir to which interfaces may release heat through a mechanism that allows fast and slow degrees to maintain their statistical properties independent.

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arXiv2011

Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses

This article is a contribution to the understanding of fluctuations in the out of equilibrium dynamics of glassy systems. By extending theoretical ideas based on the assumption that time-reparametrization invariance develops asymptotically we deduce the scaling properties of diverse high-order correlation functions. We examine these predictions with numerical tests in a standard glassy model, the 3d Edwards-Anderson spin-glass, and in a system where time-reparametrization invariance is not expected to hold, the 2d ferromagnetic Ising model, both at low temperatures. Our results enlighten a qualitative difference between the fluctuation properties of the two models and show that scaling properties conform to the time-reparametrization invariance scenario in the former but not in the latter.

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arXiv2010

Growing length scales in aging systems

We summarize studies of growing lengths in different aging systems. The article is structured as follows. We recall the definition of a number of observables, typically correlations and susceptibilities, that give access to dynamic and static correlation lengths. We use a growing length perspective to review three out of equilibrium cases: domain growth phenomena; the evolution of Edwards-Wilkinson and Kardar-Parisi-Zhang manifolds and other directed elastic manifolds in random media; spin and structural glasses in relaxation and under an external drive. Finally, we briefly report on a mechanism for dynamic fluctuations in aging systems that is based on a time-reparametrization invariance scenario and may be at the origin of the dynamic growing length in glassy materials.

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arXiv2010

Fluctuations of two-time quantities and non-linear response functions

We study the fluctuations of the autocorrelation and autoresponse functions and, in particular, their variances and co-variance. In a first general part of the Article, we show the equivalence of the variance of the response function with the second-order susceptibility of a composite operator, and we derive an equilibrium fluctuation-dissipation theorem beyond-linear order relating it to the other variances. In a second part of the paper we apply the formalism to the study to non-disordered ferromagnets, in equilibrium or in the coarsening kinetics following a critical or sub-critical quench. We show numerically that the variances and the non-linear susceptibility obey scaling with respect to the coherence length $ξ$ in equilibrium, and with respect to the growing length $L(t)$ after a quench, similarly to what is known for the autocorrelation and the autoresponse functions.

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arXiv2010

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 $\sqrt 2$) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi.

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arXiv2009

Out of equilibrium dynamics of the spiral model

We study the relaxation of the bi-dimensional kinetically constrained spiral model. We show that due to the reversibility of the dynamic rules any unblocked state fully decorrelates in finite times irrespectively of the system being in the unjammed or the jammed phase. In consequence, the evolution of any unblocked configuration occurs in a different sector of phase space from the one that includes the equilibrium blocked equilibrium configurations at criticality and in the jammed phase. We argue that such out of equilibrium dynamics share many points in common with coarsening in the one-dimensional Ising model and we identify the coarsening structures that are, basically, lines of vacancies. We provide evidence for this claim by analyzing the behaviour of several observables including the density of particles and vacancies, the spatial correlation function, the time-dependent persistence and the linear response.

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arXiv2009

Fluctuations and effective temperatures in coarsening

We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called $χ$ and $C$, the averages of which %$<χ>$, $ $ yield the self linear response and correlation function. We introduce a restricted average of the $χ$'s, summing over all configurations with a given value of $C$. We find that the restricted average $<χ>_C$ obeys a scaling form, and that the slope of the scaling function approaches the universal value $X_\infty $ of the limiting effective temperature in the long-time limit and for $C\to 0$. Our results tend to confirm the expectation that time-reparametrization invariance is not realized in coarsening systems at criticality. Finally, we discuss possible experimental tests of our proposal.

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arXiv2008

Nonlinear response and fluctuation dissipation relations

A unified derivation of the off equilibrium fluctuation dissipation relations (FDR) is given for Ising and continous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDR allows to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second one, the important problem of the definition of an off equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.

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arXiv2007

The non-equilibrium response of the critical Ising model: Universal scaling properties and Local Scale Invariance

Motivated by recent numerical findings [M. Henkel, T. Enss, and M. Pleimling, J. Phys. A: Math. Gen. 39 (2006) L589] we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al., we detect discrepancies between the actual scaling behavior of the response function and the prediction of Local Scale Invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in integrated response functions. Accordingly, the scaling form predicted on the basis of Local Scale Invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.

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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.

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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.

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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.

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arXiv2006

Crossover between Ising and XY-like behavior in the off-equilibrium kinetics of the one-dimensional clock model

We study the phase-ordering kinetics following a quench to a final temperature $T_f$ of the one-dimensional p-state clock model. We show the existence of a critical value $p_c=4$, where the properties of the dynamics change. At $T_f=0$, for $p\le p_c$ the dynamics is analogous to that of the kinetic Ising model, characterized by Brownian motion and annihilation of interfaces. Dynamical scaling is obeyed with the same dynamical exponents and scaling functions of the Ising model. For $p>p_c$, instead, the dynamics is dominated by a texture mechanism analogous to the one-dimensional XY model, and dynamical scaling is violated. During the phase-ordering process at $T_f>0$, before equilibration occurs, a cross-over between an early XY-like regime and a late Ising-like dynamics is observed for $p>p_c$.

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arXiv2006

The fluctuation-dissipation relation in an Ising model without detailed balance

We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A {\bf 26}, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions which generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the non-stationary phase ordering kinetics the parametric plot of the integrated response function $χ(t,t_w)$ versus the autocorrelation function is different from that of the kinetic Ising model. However, splitting $χ(t,t_w)$ into a stationary and an aging term $χ(t,t_w)=χ_{st}(t-t_w)+χ_{ag}(t,t_w)$, we find $χ_{ag}(t,t_w)\sim t_w^{-a_χ}f(t/t_w)$, and a numerical value of $a_χ$ consistent with $a_χ=1/4$, as in the kinetic Ising model.

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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.

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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 $A<a$.

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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.

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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.

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