Biomedical subjects

Marco Zannetti

Publications and source records attributed to Marco Zannetti.

10 recordsLinked to original sources

PubMed2006

Test of local scale invariance from the direct measurement of the response function in the Ising model quenched to and below T(C).

In order to check on a recent suggestion that local scale invariance [M. Henkel, Phys. Rev. Lett. 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+/-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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PubMed2006

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 nondisordered 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 chi(t,s) approximately or = s(-a)chif(t/s), we find a(chi) consistent with the value a(chi)=0.28 found in the two-dimensional Ising model.

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PubMed2005

Correction to scaling in the response function of the two-dimensional kinetic Ising model.

The aging part Rag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form Rag(t,s)=s-(1+a)f(t/s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273+/-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 Rag(t,s). This gives a satisfactory qualitative agreement with the numerical data for Rag(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 Rag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties.

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PubMed2005

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 69, 056109 (2004)] for the field-cooled susceptibility chi(FC)(t) - chi0 approximately 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) approximately 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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PubMed2005

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 4, 1641 (1994)]. The result is quite general and holds both for dynamics with conserved and nonconserved order parameters. 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 36, 10 739 (2003)] and Ricci-Tersenghi [Phys. Rev. E 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 nonconserved 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 chi (t, t(w)) approximately equal to t(-a)(w) f (t/t(w)) , with a =0.26+/-0.01 , as previously found with a different method.

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PubMed2004

Generic features of the fluctuation dissipation relation in coarsening systems.

The integrated response function in phase-ordering systems with scalar, vector, conserved, and nonconserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution chi(ag) (t, t(w) )= tw (- a(chi) ) chi; (t/ t(w) ) we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of a(chi) in all cases considered. The primary result is that a(chi) vanishes continuously as d approaches the lower critical dimensionality d(L). This implies that (i) the existence of a nontrivial fluctuation dissipation relation and (ii) the failure of the connection between statics and dynamics are generic features of phase ordering at d(L).

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PubMed2003

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 (ZFC) magnetization in the context of phase-ordering kinetics. We explain why the retrieval of the scaling properties of R(t,s) from those of TRM and ZFC magnetization is not trivial. Preasymptotic contributions generate a long crossover in TRM, while ZFC magnetization 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 explicitly 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 magnetization 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) approximately 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. 87, 265701 (2001)], does not hold for the Ising model.

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PubMed2002

Relaxation and overlap-probability function in the spherical and mean-spherical models.

The problem of the equivalence of the spherical and mean-spherical models, which has been thoroughly studied and is understood in equilibrium, is considered anew from the dynamical point of view during the time evolution following a quench from above to below the critical temperature. It is found that there exists a crossover time t(*) approximately V(2/d) such that for t t(*) macroscopic discrepancies arise. The relation between the off equilibrium response function and the structure of the equilibrium state that usually holds for phase ordering systems is found to hold for the spherical model but not for the mean-spherical one. The latter model offers an explicit example of a system which is not stochastically stable.

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PubMed2002

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

The off-equilibrium response function chi(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 different in the two cases, the parametric plot of chi(t,t(w)) versus C(t,t(w)) is the same. While this result could be expected in higher dimensionality, where chi(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 chi(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.

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PubMed2002

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 chi(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 chi(ag)(t,t(w)) is proportional to the defect density rho(D)(t), while for d<4 it vanishes more slowly than rho(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.

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