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Eugenio Lippiello

Publications and source records attributed to Eugenio Lippiello.

67 records · Page 4Linked to original sources
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

Memory in Self Organized Criticality

Many natural phenomena exhibit power law behaviour in the distribution of event size. This scaling is successfully reproduced by Self Organized Criticality (SOC). On the other hand, temporal occurrence in SOC models has a Poisson-like statistics, i.e. exponential behaviour in the inter-event time distribution, in contrast with experimental observations. We present a SOC model with memory: events are nucleated not only as a consequence of the instantaneous value of the local field with respect to the firing threshold, but on the basis of the whole history of the system. The model is able to reproduce the complex behaviour of inter-event time distribution, in excellent agreement with experimental seismic data.

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↗