Condensation of Fluctuations in and out of Equilibrium

Condensation of fluctuations is an interesting phenomenon conceptually distinct from condensation on average. One stricking feature is that, contrary to what happens on average, condensation of fluctuations may occurr even in the absence of interaction. The explanation emerges from the duality between large deviation events in the given system and typical events in a new and appropriately biased system. This surprising phenomenon is investigated in the context of the Gaussian model, chosen as paradigmatical non interacting system, before and after an istantaneous temperature quench. It is shown that the bias induces a mean-field-like effective interaction responsible of the condensation on average. Phase diagrams, covering both the equilibrium and the off-equilibrium regimes, are derived for observables representative of generic behaviors.Comment: 8 pages, 7 figure

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 $\chi_{FC}(t) - \chi_0 \sim t^{-A}$ 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 $A<a$.Comment: 4 pages, 4 figure

Roughening of an interface in a system with surface or bulk disorder

We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also away from it, in the bulk. The dynamical structure factor shows a rich crossover pattern from the form of a pure system at large wavevectors $k$, to a different behavior, typical of the kind of disorder, at smaller $k$'s. For the random field model a second crossover is observed from the typical behavior of a system where disorder is only effective on the surface, as the random bond model, to the truly large scale behavior, where bulk-disorder is important, that is observed at the smallest wavevectors.Comment: 13 pages, 8 figure

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.Godr\`{e}che and J.M.Luck, Phys.Rev.Lett. {\bf 87}, 265701 (2001)], does not hold for the Ising model.Comment: 26 pages, 14 figure

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 $\chi (t,t_w)\simeq t_w^{-a}f(t/t_w)$, with $a =0.26\pm 0.01$, as previously found with a different method.Comment: 12 pages, 5 figure

Phase ordering in 3d disordered systems

We study numerically the phase-ordering kinetics of the site-diluted and bond-diluted Ising models after a quench from an infinite to a low temperature. We show that the speed of growth of the ordered domain's size is non-monotonous with respect to the amount of dilution $D$: Starting from the pure case $D=0$ the system slows down when dilution is added, as it is usually expected when disorder is introduced, but only up to a certain value $D^*$ beyond which the speed of growth raises again. We interpret this counterintuitive fact in a renormalization-group inspired framework, along the same lines proposed for the corresponding two-dimensional systems, where a similar pattern was observed.Comment: 8 pages, 4 figures.To appear on Journal of Statistical Mechanics: Theory and Experiment. arXiv admin note: text overlap with arXiv:1306.514

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.Comment: 17 pages, 5 figures. To appear in Phys. Rev.