arXiv subjects

Eugenio Lippiello

Publications and source records attributed to Eugenio Lippiello.

At least 37 records · Page 2Linked to original sources

arXiv2020

Kinetics of the Two-dimensional Long-range Ising Model at Low Temperatures

We study the low-temperature domain growth kinetics of the two-dimensional Ising model with long-range coupling: $J(r) \sim r^{-(d+σ)}$, where $d=2$ is the dimensionality. According to the Bray-Rutenberg predictions, the exponent $σ$ controls the algebraic growth in time of the characteristic domain size $L(t)$, $L(t) \sim t^{1/z}$, with growth exponent $z=1+σ$ for $σ<1$ and $z=2$ for $σ>1$. These results hold for quenches to a non-zero temperature $T>0$ below the critical temperature $T_c$. We show that, in the case of quenches to $T=0$, due to the long-range interactions, the interfaces experience a drift which makes the dynamics of the system peculiar. More precisely we find that in this case the growth exponent takes the value $z=4/3$, independent of $σ$, showing that it is a universal quantity. We support our claim by means of extended Monte Carlo simulations and analytical arguments for simplified models.

cond-mat.stat-mech↗

arXiv2020

Quasi-deterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets

We discuss the interplay between the degree of dynamical stochasticity, memory persistence and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasi-deterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including mean-field, and the short-range random field Ising model.

cond-mat.stat-mech↗

arXiv2020

The influence of the brittle-ductile transition zone on aftershock and foreshock occurrence

Aftershock occurrence is characterized by scaling behaviors with quite universal exponents. At the same time, deviations from universality have been proposed as a tool to discriminate aftershocks from foreshocks. Here we show that the change in rheological behavior of the crust, from velocity weakening to velocity strengthening, represents a viable mechanism to explain statistical features of both aftershocks and foreshocks. More precisely, we present a model of the seismic fault described as a velocity weakening elastic layer coupled to a velocity strengthening visco-elastic layer. We show that the statistical properties of aftershocks in instrumental catalogs are recovered at a quantitative level, quite independently of the value of model parameters. We also find that large earthquakes are often anticipated by a preparatory phase characterized by the occurrence of foreshocks. Their magnitude distribution is significantly flatter than the aftershock one, in agreement with recent results for forecasting tools based on foreshocks.

physics.geo-ph↗

arXiv2020

Growth Kinetics and Aging Phenomena in a Frustrated System

We study numerically the ordering kinetics in a two-dimensional Ising model with random coupling where the fraction of antiferromagnetic links $a$ can be gradually tuned. We show that, upon increasing such fraction, the behavior changes in a radical way. Small $a$ does not prevent the system from a complete ordering, but this occurs in an extremely (logarithmically) slow manner. However, larger values of this parameter destroy complete ordering, due to frustration, and the evolution is comparatively faster (algebraic). Our study shows a precise correspondence between the kind of developing order, ferromagnetic versus frustrated, and the speed of evolution. The aging properties of the system are studied by focusing on the scaling properties of two-time quantities, the autocorrelation and linear response functions. We find that the contribution of equilibrium and an aging part to these functions occurs differently in the various regions of the phase diagram of the model. When quenching inside the ferromagnetic phase, the two-time quantities are obtained by the addition of these parts. Instead, in the paramagnetic phase, these two contributions enter multiplicatively. Both of the scaling forms are shown with excellent accuracy, and the corresponding scaling functions and exponents have been determined and discussed.

cond-mat.stat-mech↗

arXiv2019

Universality in the time correlations of the long-range 1d Ising model

The equilibrium and nonequilibrium properties of ferromagnetic systems may be affected by the long-range nature of the coupling interaction. Here we study the phase separation process of a one-dimensional Ising model in the presence of a power-law decaying coupling, $J(r)=1/r^{1+σ}$ with $σ>0$, and we focus on the two-time autocorrelation function $C(t,t_w)=\langle s_i(t) s_i(t_w)\rangle$. We find that it obeys the scaling form $C(t,t_w)=f(L(t_w)/L(t))$, where $L(t)$ is the typical domain size at time $t$, and where $f(x)$ can only be of two types. For $σ>1$, when domain walls diffuse freely, $f(x)$ falls in the nearest-neighbour (nn) universality class. Conversely, for $σ\le 1$, when domain walls dynamics is driven, $f(x)$ displays a new universal behavior. In particular, the so-called Fisher-Huse exponent, which characterizes the asymptotic behavior of $f(x)\simeq x^{-λ}$ for $x\gg 1$, is $λ=1$ in the nn universality class ($σ> 1$) and $λ=1/2$ for $σ\le 1$.

cond-mat.stat-mech↗

arXiv2019

One dimensional phase-ordering in the Ising model with space decaying interactions

The study of the phase ordering kinetics of the ferromagnetic one-dimensional Ising model dates back to 1963 for non conserved order parameter (NCOP) and to 1991 for conserved order parameter (COP). The case of long range interactions $J(r)$ has been widely studied at equilibrium but their effect on relaxation is a much less investigated field. Here we make a detailed numerical and analytical study of both cases, NCOP and COP. Many results are valid for any positive, decreasing coupling $J(r)$, but we focus specifically on the exponential case, $J_{exp}(r)=e^{-r/R}$ with varying $R>0$, and on the integrable power law case, $J_{pow}(r) =1/r^{1+σ}$ with $σ> 0$. We find that the {\it asymptotic} growth law $L(t)$ is the usual algebraic one, $L(t)\sim t^{1/z}$, of the corresponding model with nearest neighborg interaction ($z_{NCOP}=2$ and $z_{COP}=3$) for all models except $J_{pow}$ for small $σ$: in the non conserved case when $σ\le 1$ ($z_{NCOP}=σ+1$) and in the conserved case when $σ\to 0^+$ ($z_{COP}=4β+3$, where $β=1/T$ is the inverse of the absolute temperature). The models with space decaying interactions also differ markedly from the ones with nearest neighbors due to the presence of many long-lasting preasymptotic regimes, such as an exponential mean-field behavior with $L(t)\sim e^{t}$, a ballistic one with $L(t)\sim t$, a slow (logarithmic) behavior $L(t)\sim \ln t$ and one with $L(t)\sim t^{1/σ+1}$. All these regimes and their validity ranges have been found analytically and verified in numerical simulations. Our results show that the main effect of the conservation law is a strong slowdown of COP dynamics if interactions have an extended range. Finally, we compare the Ising model at hand with continuum approaches based on a Ginzburg-Landau free energy.

cond-mat.stat-mech↗

arXiv2019

Effects of Frustration on Fluctuation-dissipation Relations

We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)], where frustration can be tuned by varying the fraction a of antiferromagnetic interactions. Specifically we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems.

cond-mat.stat-mech↗

arXiv2018

Fault heterogeneity and the connection between aftershocks and afterslip

Whether aftershocks originate directly from the mainshock and surrounding stress environment or from afterslip dynamics is crucial to the understanding of the nature of aftershocks. We build on a classical description of the fault and creeping regions as two blocks connected elastically, subject to different friction laws. We show analytically that, upon introduction of variability in the fault plane's static friction threshold, a non trivial stick-slip dynamics ensues. In particular we support the hypothesis \citep{PA04} that the aftershock occurrence rate is proportional to the afterslip rate, up to a corrective factor that is also computed. Thus, the Omori law originates from the afterslip's logarithmic evolution in the velocity-strengthening region. We confirm these analytical results with numerical simulations, generating synthetic catalogs with statistical features in good agreement with instrumental catalogs. In particular we recover the Gutenberg-Richter law with a realistic $b$-value ($b\simeq 1$) when Coulomb stress thresholds obey a power law distribution.

physics.geo-ph↗

arXiv2017

Rattler-induced aging dynamics in jammed granular systems

Granular materials jam when developing a network of contact forces able to resist the applied stresses. Through numerical simulations of the dynamics of the jamming process, we show that the jamming transition does not occur when the kinetic energy vanishes. Rather, as the system jams, the kinetic energy becomes dominated by rattlers particles, that scatter withing their cages. The relaxation of the kinetic energy in the jammed configuration exhibits a double power-law decay, which we interpret in terms of the interplay between backbone and rattlers particles.

cond-mat.stat-mech↗

arXiv2017

Effective mobility and diffusivity in coarsening processes

We suggest that coarsening dynamics can be described in terms of a generalized random walk, with the dynamics of the growing length $L(t)$ controlled by a drift term, $μ(L)$, and a diffusive one, ${\cal D}(L)$. We apply this interpretation to the one dimensional Ising model with a ferromagnetic coupling constant decreasing exponentially on the scale $R$. In the case of non conserved (Glauber) dynamics, both terms are present and their balance depend on the interplay between $L(t)$ and $R$. In the case of conserved (Kawasaki) dynamics, drift is negligible, but ${\cal D}(L)$ is strongly dependent on $L$. The main pre-asymptotic regime displays a speeding of coarsening for Glauber dynamics and a slowdown for Kawasaki dynamics. We reason that a similar behaviour can be found in two dimensions.

cond-mat.stat-mech↗

arXiv2017

Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration

We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction $a$ of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of $a$, $a a_a$ an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of $a$. We show that different amounts of frustration, tuned by $a$, affect the dynamical properties in a highly non trivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e. algebraic, when spin glass order is prevailing. An interpretation is given in terms of the different nature of phase space.

cond-mat.stat-mech↗

arXiv2016

On a relation between roughening and coarsening

We argue that a strict relation exists between two in principle unrelated quantities: The size of the growing domains in a coarsening system, and the kinetic roughening of an interface. This relation is confirmed by extensive simulations of the Ising model with different forms of quenched disorder, such as random bonds, random fields and stochastic dilution.

cond-mat.stat-mech↗

arXiv2016

Solid-on-solid single block dynamics under mechanical vibration

The suppression of friction between sliding objects, modulated or enhanced by mechanical vibrations, is well established. However, the precise conditions of occurrence of these phenomena is not well understood. Here we address these questions focusing on a simple spring--block model, which is relevant to investigate friction both at the atomistic as well as the macroscopic scale. This allows to investigate the influence on friction of the properties of the external drive, of the geometry of the surfaces over which the block moves, and of the confining force. Via numerical simulations and a theoretical study of the equations of motion we identify the conditions under which friction is suppressed and/or recovered, and evidence the critical role played by surface modulations and by the properties of the confining force.

cond-mat.soft↗

arXiv2016

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.

cond-mat.stat-mech↗

arXiv2016

Dynamic weakening by acoustic fluidization during stick-slip motion

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering.

cond-mat.stat-mech↗

arXiv2015

Non-monotonic dependence of the friction coefficient on heterogeneous stiffness

The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on loading conditions, the real area of contact along the interfaces and the confining pressure. Here we show, by means of numerical simulations of a 2D Burridge-Knopoff model with a simple local friction law, that the macroscopic friction coefficient depends non-monotonically on the bulk elasticity of the system. This occurs because elastic constants control the geometrical features of the rupture fronts during the stick-slip dynamics, leading to four different ordering regimes characterized by different orientations of the rupture fronts with respect to the external shear direction. We rationalize these results by means of an energetic balance argument.

cond-mat.stat-mech↗

arXiv2015

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.

cond-mat.stat-mech↗

arXiv2015

Phase ordering in disordered and inhomogeneous systems

We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth-laws of the ordered domains size - logarithmic or power-law respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature which governs the presence or the absence of a finite-temperature phase-transition.

cond-mat.stat-mech↗