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We determine the dimensional dependence of the percolative exponents of the jamming transition via numerical simulations in four and five spatial dimensions. These novel results complement literature ones, and establish jamming as a mixed first-order percolation transition, with critical exponents $\beta =0$, $\gamma = 2$, $\alpha = 0$ and the finite size scaling exponent $\nu^* = 2/d$ for values of the spatial dimension $d \geq 2$. We argue that the upper critical dimension is $d_u=2$ and the connectedness length exponent is $\nu =1$., Comment: 11 pages, 3 figures, VSI of Physica A in memory of Dietrich Stauffer

The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to insure ergodicity breaking in the low temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e. there exists a well defined asymptotic state which is time-invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state, by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable one from the other. However while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly., Comment: 18 pages, 9 figures

The ferromagnetic transition in the Ising model is the paradigmatic example of ergodicity breaking accompanied by symmetry breaking. It is routinely assumed that the thermodynamic limit is taken with free or periodic boundary conditions. More exotic symmetry-preserving boundary conditions, like cylindrical antiperiodic, are less frequently used for special tasks, such as the study of phase coexistence or the roughening of an interface. Here we show, instead, that when the thermodynamic limit is taken with these boundary conditions, a novel type of transition takes place below $T_c$ (the usual Ising transition temperature) without breaking neither ergodicity nor symmetry. Then, the low temperature phase is characterized by a regime (condensation) of strong magnetization's fluctuations which replaces the usual ferromagnetic ordering. This is due to critical correlations perduring for all T below Tc. The argument is developed exactly in the $d=1$ case and numerically in the d=2 case., 13 pages, 10 figures

The dynamical facilitation scenario, by which localized relaxation events promote nearby relaxation events in an avalanching process, has been suggested as the key mechanism connecting the microscopic and the macroscopic dynamics of structural glasses. Here we investigate the statistical features of this process via the numerical simulation of a model structural glass. First we show that the relaxation dynamics of the system occurs through particle jumps that are irreversible, and that cannot be decomposed in smaller irreversible events. Then we show that each jump does actually trigger an avalanche. The characteristic of this avalanche change on cooling, suggesting that the relaxation dynamics crossovers from a noise dominated regime where jumps do not trigger other relaxation events, to a regime dominated by the facilitation process, where a jump trigger more relaxation events., Comment: 8 pages, 6 figures

The mechanical and transport properties of jammed materials originate from an underlying per- colating network of contact forces between the grains. Using extensive simulations we investigate the force-percolation transition of this network, where two particles are considered as linked if their interparticle force overcomes a threshold. We show that this transition belongs to the random percolation universality class, thus ruling out the existence of long-range correlations between the forces. Through a combined size and pressure scaling for the percolative quantities, we show that the continuous force percolation transition evolves into the discontinuous jamming transition in the zero pressure limit, as the size of the critical region scales with the pressure., Comment: 5 pages, 5 figures

The evaluation of the long term stability of a material requires the estimation of its long-time dynamics. For amorphous materials such as structural glasses, it has proven difficult to predict the long-time dynamics starting from static measurements. Here we consider how long one needs to monitor the dynamics of a structural glass to predict its long--time features. We present a detailed characterization of the statistical features of the single-particle intermittent motion of structural glasses, and show that single--particle jumps are the irreversible events leading to the relaxation of the system. This allows to evaluate the diffusion constant on the time--scale of the jump duration, which is small and temperature independent, well before the system enters the diffusive regime. The prediction is obtained by analyzing the particle trajectories via a parameter-free algorithm., Comment: 6 pages, 5 figures, accepted for publication in Soft Matter (21 May 2014)

We investigate the heterogeneous dynamics in a model, where chemical gelation and glass transition interplay, focusing on the dynamical susceptibility. Two independent mechanisms give raise to the correlations, which are manifested in the dynamical susceptibility: one is related to the presence of permanent clusters, while the other is due to the increase of particle crowding as the glass transition is approached. The superposition of these two mechanisms originates a variety of different behaviours. We show that these two mechanisms can be unentangled considering the wave vector dependence of the dynamical susceptibility., Comment: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60175-x

Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are within those systems known to exhibit a discontinuous dynamical transition with a two step relaxation. We consider a general scaling approach, within mean field theory, for such systems by considering the behavior of the density correlator and the dynamical susceptibility -^2. Focusing on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe lattice, we extend a cluster approach that was previously developed for continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R) (2014)) to describe the decay to the plateau, and consider a damage spreading mechanism to describe the departure from the plateau. We predict scaling laws, which relate dynamical exponents to the static exponents of mean field bootstrap percolation. The dynamical behavior and the scaling laws for both density correlator and dynamical susceptibility coincide with those predicted by MCT. These results explain the origin of scaling laws and the universal behavior associated with the glass transition in mean field, which is characterized by the divergence of the static length of the bootstrap percolation model with an upper critical dimension d_c=8., Comment: 16 pages, 9 figures

We perform molecular dynamic (MD) simulations of frictional non-thermal particles driven by an externally applied shear stress. After the system jams following a transient flow, we probe its mechanical response in order to clarify whether the resulting solid is 'fragile'. We find the system to respond elastically and isotropically to small perturbations of the shear stress, suggesting absence of fragility. These results are interpreted in terms of the energy landscape of dissipative systems. For the same values of the control parameters, we check the behaviour of the system during a stress cycle. Increasing the maximum stress value, a crossover from a visco-elastic to a plastic regime is observed., 6 pages, 9 figures, accepted in Granular Matter on 01-02-2012

Particles in structural glasses rattle around temporary equilibriumpositions, that seldom change through a process which is much faster than the relaxation time, known as particle jump. Since the relaxation of the system is due to the accumulation of many such jumps, it could be possible to connect the single particle short time motion to the macroscopic relaxation by understanding the features of the jump dynamics. Here we review recent results in this research direction, clarifying the features of particles jumps that have been understood and those that are still under investigation, and examining the role of particle jumps in different theories of the glass transition., Comment: 10 pages, 4 figures, Review article

We show that the relaxation dynamics near a glass transition with continuous ergodicity breaking can be endowed with a geometric interpretation based on percolation theory. At the mean-field level this approach is consistent with the mode-coupling theory (MCT) of type-A liquid-glass transitions and allows one to disentangle the universal and nonuniversal contributions to MCT relaxation exponents. Scaling predictions for the time correlation function are successfully tested in the ${\mathsf{F}}_{12}$ schematic model and facilitated spin systems on a Bethe lattice. Our approach immediately suggests the extension of MCT scaling laws to finite spatial dimensions and yields predictions for dynamic relaxation exponents below an upper critical dimension of 6.

In this paper we study the 3d frustrated lattice gas model in the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint. Although the model does not exhibit any thermodynamic transition it shows a diverging peak at some characteristic time in the dynamical non-linear susceptibility, similar to the results on the p-spin model in mean field and Lennard-Jones mixture recently found by Donati et al. [cond-mat/9905433]. Comparing these results to those obtained in the model with quenched interactions, we conclude that the critical behavior of the dynamical susceptibility is reminiscent of the thermodynamic transition present in the quenched model, and signaled by the divergence of the static non-linear susceptibility, suggesting therefore a similar mechanism also in supercooled glass-forming liquids., 8 pages, 14 figures

We briefly review the basics ideas and results of a recently proposed statistical mechanical approach to granular materials. Using lattice models from standard Statistical Mechanics and results from a mean field replica approach and Monte Carlo simulations we find a jamming transition in granular media closely related to the glass transition in super-cooled liquids. These models reproduce the logarithmic relaxation in granular compaction and reversible-irreversible lines, in agreement with experimental data. The models also exhibit aging effects and breakdown of the usual fluctuation dissipation relation. It is shown that the glass transition may be responsible for the logarithmic relaxation and may be related to the cooperative effects underlying many phenomena of granular materials such as the Reynolds transition., 18 pages with 6 postscript figures. to appear in J.Phys: Cond. Mat

To understand the origin of the dynamical transition, between high temperature exponential relaxation and low temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in presence of disorder) or fully frustrated Ising (in absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case., Comment: Completely rewritten. New data. New results

The dynamical arrest of gels is the consequence of a well defined structural phase transition, leading to the formation of a spanning cluster of bonded particles. The dynamical glass transition, instead, is not accompanied by any clear structural signature. Nevertheless, both transitions are characterized by the emergence of dynamical heterogeneities. Reviewing recent results from numerical simulations, we discuss the behavior of dynamical heterogeneities in different systems and show that a clear connection with the structure exists in the case of gels. The emerging picture may be also relevant for the more elusive case of glasses. We show, as an example, that the relaxation process of a simple glass-forming model can be related to a reverse percolation transition and discuss further perspective in this direction., Published in the J. Stat. Mech. Special Issue of "The Role of Structure in Glassy and Jammed Systems "

The sluggish and heterogeneous dynamics of glass forming liquids is frequently associated to the transient coexistence of two phases of particles, respectively with an high and low mobility. In the absence of a dynamical order parameter that acquires a transient bimodal shape, these phases are commonly identified empirically, which makes difficult investigating their relation with the structural properties of the system. Here we show that the distribution of single particle diffusivities can be accessed within a Continuous Time Random Walk description of the intermittent motion, and that this distribution acquires a transient bimodal shape in the deeply supercooled regime, thus allowing for a clear identification of the two coexisting phase. In a simple two-dimensional glass forming model, the dynamic phase coexistence is accompanied by a striking structural counterpart: the distribution of the crystalline-like order parameter becomes also bimodal on cooling, with increasing overlap between ordered and immobile particles. This simple structural signature is absent in other models, such as the three-dimesional Kob-Andersen Lennard-Jones mixture, where more sophisticated order parameters might be relevant. In this perspective, the identification of the two dynamical coexisting phases opens the way to deeper investigations of structure-dynamics correlations., Comment: Published in the J. Stat. Mech. Special Issue "The Role of Structure in Glassy and Jammed Systems"

We investigate the relaxation process and the dynamical heterogeneities of the kinetically constrained Kob-Andersen lattice glass model and show that these are characterized by different time scales. The dynamics is well described within the diffusing defect paradigm, which suggests that we relate the relaxation process to a reverse-percolation transition. This allows for a geometrical interpretation of the relaxation process and of the different time scales.

The non-equilibrium transition from a fluid-like state to a disordered solid-like state, known as the jamming transition, occurs in a wide variety of physical systems, such as colloidal suspensions and molecular fluids, when the temperature is lowered or the density increased. Shear stress, as temperature, favors the fluid-like state, and must be also considered to define the system 'jamming phase diagram' [1-4]. Frictionless athermal systems [1], for instance, can be described by the zero temperature plane of the jamming diagram in the temperature, density, stress space. Here we consider the jamming of athermal frictional systems [8-13] such as granular materials, which are important to a number of applications from geophysics to industry. At constant volume and applied shear stress[1, 2], we show that while in absence of friction a system is either fluid-like or jammed, in the presence of friction a new region in the density shear-stress plane appears, where new dynamical regimes are found. In this region a system may slip, or even flow with a steady velocity for a long time in response to an applied stress, but then eventually jams. Jamming in non-thermal frictional systems is described here by a phase diagram in the density, shear-stress and friction space.

A theoretical and numerically study of dynamical properties in the sol-gel transition is presented. In particular, the complex phenomenology observed experimentally and numerically in gelling systems is reproduced in the framework of percolation theory, under simple assumptions on the relaxation of single clusters. By neglecting the correlation between particles belonging to different clusters, the quantities of interest (such as the self intermediate scattering function, the dynamical susceptibility, the Van-Hove function, and the non-Gaussian parameter) are written as superposition of those due to single clusters. Connection between these behaviors and the critical exponents of percolation are given. The theoretical predictions are checked in a model for permanent gels, where bonds between monomers are described by a finitely extendable nonlinear elastic potential. The data obtained in the numerical simulations are in good agreement with the analytical predictions., 23 pages, 8 figures

We present a theoretical study of a system with competing short-range ferromagnetic attraction and a long-range anti-ferromagnetic repulsion, in the presence of a uniform external magnetic field. The interplay between these interactions, at sufficiently low temperature, leads to the self-tuning of the magnetization to a value which triggers phase coexistence, even in the presence of the external field. The investigation of this phenomenon is performed using a Ginzburg-Landau functional in the limit of an infinite number of order parameter components (large $N$ model). The scalar version of the model is expected to describe the phase separation taking place on a cell surface when this is immersed in a uniform concentration of chemical stimulant. A phase diagram is obtained as function of the external field and the intensity of the long-range repulsion. The time evolution of order parameter and of the structure factor in a relaxation process are studied in different regions of the phase diagram., new title and largely revised version, to be published in Phys.Rev. E

Via molecular dynamics simulations, we unveil the hysteretic nature of the jamming transition of soft repulsive frictionless spheres, as it occurs varying the volume fraction or the shear stress. In a given range of control parameters the system may be found both in a flowing and in an jammed state, depending on the preparation protocol. The hysteresis is due to an underlying energy landscape with many minima, as explained by a simple model, and disappears in the presence of strong viscous forces and in the small $\sigma$ limit. In this limit, structural quantities are continuous at the transition, while the asymptotic values of two time quantities such as the self-intermediate scattering function are discontinuous, giving to the jamming transition a mixed first-order second-order character close to that found at the glass transition of thermal systems.

The most costly and annoying characteristic of the e-mail communication system is the large number of unsolicited commercial e-mails, known as spams, that are continuously received. Via the investigation of the statistical properties of the spam delivering intertimes, we show that spams delivered to a given recipient are time correlated: if the intertime between two consecutive spams is small (large), then the next spam will most probably arrive after a small (large) intertime. Spam temporal correlations are reproduced by a numerical model based on the random superposition of spam sequences, each one described by the Omori law. This and other experimental findings suggest that statistical approaches may be used to infer how spammers operate., Europhysics Letters, to appear

We study the rheological properties of a granular suspension subject to constant shear stress by constant volume molecular dynamics simulations. We derive the system `flow diagram' in the volume fraction/stress plane $(\phi,F)$: at low $\phi$ the flow is disordered, with the viscosity obeying a Bagnold-like scaling only at small $F$ and diverging as the jamming point is approached; if the shear stress is strong enough, at higher $\phi$ an ordered flow regime is found, the order/disorder transition being marked by a sharp drop of the viscosity. A broad jamming region is also observed where, in analogy with the glassy region of thermal systems, slow dynamics followed by kinetic arrest occurs when the ordering transition is prevented., Comment: 4 pages

In this paper we present a detailed analytical study of the phase diagram and of the structural properties of a field theoretic model with a short-range attraction and a competing long-range screened repulsion. We provide a full derivation and expanded discussion and digression on results previously reported briefly in M. Tarzia and A. Coniglio, Phys. Rev. Lett. 96, 075702 (2006). The model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions. We employ the self-consistent Hartree approximation and a replica approach, and we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales, and emphasize that the formation of microphase structures may play a prominent role in the process of colloidal gelation., 16 pages, 7 figures

We study the formation of a colloidal gel by means of Molecular Dynamics simulations of a model for colloidal suspensions. A slowing down with gel-like features is observed at low temperatures and low volume fractions, due to the formation of persistent structures. We show that at low volume fraction the dynamic susceptibility, which describes dynamic heterogeneities, exhibits a large plateau, dominated by clusters of long living bonds. At higher volume fraction, where the effect of the crowding of the particles starts to be present, it crosses over towards a regime characterized by a peak. We introduce a suitable mean cluster size of clusters of monomers connected by "persistent" bonds which well describes the dynamic susceptibility., Comment: 4 pages, 4 figures

The compaction dynamics of a granular media subject to a sequence of vertical taps made of fluid pulses is investigated via Molecular Dynamics simulations. Our study focuses on three different levels: macroscopic (volume fraction), mesoscopic (Vorono\"{\i} volumes, force distributions) and microscopic (grain displacements). We show that the compaction process has many characteristics which are reminiscent of the slow dynamics of glass forming systems, as previously suggested. For instance the mean volume fraction slowly increases in time and approaches a stationary value following a stretched exponential law, and the associated compaction time diverges as the tapping intensity decreases. The study of microscopic quantities also put in evidence the existence of analogies with the dynamics of glass formers, as the existence of dynamical heterogeneities and spatially correlated motion of grains; however it also shows that there are important qualitative differences, as for instance in the role of the cage effect. Correlations between geometry and dynamics of the system at the grain level are put in evidence by comparing a particle Vorono\"{\i} volume and its displacement in a single tap.

We discuss the microscopic origin of dynamical instabilities and segregation patterns discovered in granular mixtures under oscillating horizontal shear, by investigating, via molecular dynamics simulations, the effective interaction between like-particles. This turns out to be attractive at short distances and strongly anisotropic, with a longer range repulsive shoulder along the direction of oscillation. This features explain the system rich phenomenology, including segregation and stripe pattern formation. Finally, we show that a modified Cahn-Hilliard equation, taking into account the characteristics of the effective interaction, is capable of describing the dynamics of the mixture.

By detailed Molecular Dynamics and Monte Carlo simulations %of a realistic model we show that granular materials at rest can be described as thermodynamics systems. First we show that granular packs can be characterized by few parameters, as much as fluids or solids. Then, in a second independent step, we demonstrate that these states can be described in terms of equilibrium distributions which coincide with the Statistical Mechanics of powders first proposed by Edwards. We also derive the system equation of state as a function of the ``configurational temperature'', its new intensive thermodynamic parameter., Comment: Supplementary Informations added

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism which gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from Brasil nut to reverse Brasil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps., Submitted to Phys. Rev. Lett

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature., Comment: 11 pages, 12 figures

A scaling theory is used to derive the dependence of the average number of spanning clusters at threshold on the lattice size L. This number should become independent of L for dimensions d6 depend on the boundary conditions, and the results there may vary between L^{d-6} and L^0. While simulations in six dimensions are consistent with this prediction (after including corrections of order loglog L), in five dimensions the average number of spanning clusters still increases as log L even up to L = 201. However, the histogram P(k) of the spanning cluster multiplicity does scale as a function of kX(L), with X(L)=1+const/L, indicating that for sufficiently large L the average will approach a finite value: a fit of the 5D multiplicity data with a constant plus a simple linear correction to scaling reproduces the data very well. Numerical simulations for d>6 and for d=4 are also presented., 8 pages, 11 figures. Final version to appear on Physical Review E

We introduce and analytically study a generalized $p$-spin glasslike model that captures some of the main features of attractive glasses, recently found by mode coupling investigations, such as a glass-glass transition line and dynamical singularity points characterized by a logarithmic time dependence of the relaxation. The model also displays features not predicted by the mode coupling scenario that could further describe the attractive glasses behavior, such as aging effects with new dynamical singularity points ruled by logarithmic laws or the presence of a glass spinodal line.

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and we focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally., to appear on Physical Review Letters

We address the question of the dependence of the fragility of glass forming supercooled liquids on the softness of an interacting potential by performing numerical simulation of a binary mixture of soft spheres with different power n of the interparticle repulsive potential. We show that the temperature dependence of the diffusion coefficients for various $n$ collapses onto a universal curve, supporting the unexpected view that fragility is not related to the hard core repulsion. We also find that the configurational entropy correlates with the slowing down of the dynamics for all studied n., Comment: 4 pages, 4 figures

Dynamical instabilities in fluid mechanics are responsible of a variety of important common phenomena, such as waves on the sea surface or Taylor vorteces in Couette flow. In granular media dynamical instabilities has just begun to be discovered. Here we show by means of molecular dynamics simulation the existence of a new dynamical instability of a granular mixture under oscillating horizontal shear, which leads to the formation of a striped pattern where the components are segregated. We investigate the properties of such a Kelvin-Helmholtz like instability and show how it is connected to pattern formation in granular flow and segregation., Comment: Phys. Rev. Lett. 94, 188001

We here discuss the results of 3d MonteCarlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics, investigated by means of the time autocorrelation function of the density fluctuations and the particle mean square displacement. We start from the case of chemical gelation, i.e. with permanent bonds, we characterize the critical dynamics as determined by the formation of the percolating cluster, as actually observed in polymer gels. By opportunely introducing a finite bond life time $\tau_b$ the dynamics displays relevant changes and eventually the onset of a glassy regime. This has been interpreted in terms of a crossover to dynamics more typical of colloidal systems and a novel connection between classical gelation and recent results on colloidal systems is suggested. By systematically comparing the results in the case of permanent bonds to finite bond lifetime, the crossover and the glassy regime can be understood in terms of effective clusters., Comment: 14 pages, 13 figures, to appear in Physical Review E

We introduce a spherical version of the frustrated Blume-Emery-Griffiths model and solve exactly the statics and the Langevin dynamics for zero particle-particle coupling (K=0). In this case the model exhibits an equilibrium transition from a disordered to a spin glass phase which is always continuous for nonzero temperature. The same phase diagram results from the study of the dynamics. Furthermore, we notice the existence of a nonequilibrium time regime in a region of the disordered phase, characterized by aging as occurs in the spin glass phase. Due to a finite equilibration time, the system displays in this region the pattern of interrupted aging., Comment: 19 pages, 8 figures

The number of spanning clusters in four to nine dimensions does not fully follow the expected size dependence for random percolation., Comment: 9-dimensional data and more points for large lattices added; statistics improved, text expanded, table of exponents inserted

We discuss a Statistical Mechanics approach in the manner of Edwards to the ``inherent states'' (defined as the stable configurations in the potential energy landscape) of glassy systems and granular materials. We show that at stationarity the inherent states are distributed according a generalized Gibbs measure obtained assuming the validity of the principle of maximum entropy, under suitable constraints. In particular we consider three lattice models (a diluted Spin Glass, a monodisperse hard-sphere system under gravity and a hard-sphere binary mixture under gravity) undergoing a schematic ``tap dynamics'', showing via Monte Carlo calculations that the time average of macroscopic quantities over the tap dynamics and over such a generalized distribution coincide. We also discuss about the general validity of this approach to non thermal systems., Comment: 10 pages, 16 figures

In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation and critical behaviour in the Ising model, one might check whether the breakdown of hyperscaling in the Ising model can also be intepreted as due to an infinite multiplicity of percolating Fortuin-Kasteleyn clusters at the critical temperature T_c. Preliminary results suggest that the scenario is much more involved than expected due to the fact that the percolation variables behave differently on the two sides of T_c., Lattice2002(spin)

We perform large scale simulations of the frustrated Ising lattice gas, a three-dimensional lattice model of a structural glass, using the parallel tempering technique. We evaluate the spin and density overlap distributions, and the corresponding non-linear susceptibilities, as a function of the chemical potential. We then evaluate the relaxation functions of the spin and density self-overlap, and study the behavior of the relaxation times. The results suggest that the spin variables undergo a transition very similar to the one of the Ising spin glass, while the density variables do not show any sign of transition at the same chemical potential. It may be that the density variables undergo a transition at a higher chemical potential, inside the phase where the spins are frozen., 7 pages, 10 figures

We study the relaxation process in a two-dimensional lattice gas model, where the interactions come from the excluded volume. In this model particles have three arms with an asymmetrical shape, which results in geometrical frustration that inhibits full packing. A dynamical crossover is found at the arm percolation of the particles, from a dynamical behavior characterized by a single step relaxation above the transition, to a two-step decay below it. Relaxation functions of the self-part of density fluctuations are well fitted by a stretched exponential form, with a $\beta$ exponent decreasing when the temperature is lowered until the percolation transition is reached, and constant below it. The structural arrest of the model seems to happen only at the maximum density of the model, where both the inverse diffusivity and the relaxation time of density fluctuations diverge with a power law. The dynamical non linear susceptibility, defined as the fluctuations of the self-overlap autocorrelation, exhibits a peak at some characteristic time, which seems to diverge at the maximum density as well., Comment: 7 pages and 9 figures

The present paper proposes a Statistical Mechanics approach to the inherent states of glassy systems and granular materials, following the original ideas developed by Edwards for granular materials. Two lattice models, a diluted Spin Glass and a system of hard-spheres under gravity, introduced in the context of glassy systems and granular materials, are evolved using a ``tap dynamics'' analogous to that of experiments on granular materials. The asymptotic macrostates, reached by the system, are shown to be described by a single thermodynamical parameter, and this parameter to coincide with the temperature, called the ``configurational temperature'', predicted assuming that the distribution among the inherent states satisfies the principle of maximum entropy., Comment: revised and improved version including new results on a 3D hard-spheres model; 4 pages, 4 figures

Similarities between fragile glasses and spin glasses (SG) suggest the study of frustrated spin model to understand the complex dynamics of glasses above the glass transition. We consider a frustrated spin model with Ising spins and s-state Potts spins both with and without disorder. We study the two models by Monte Carlo simulations in two dimensions. The Potts spins mimic orientational degrees of freedom and the coupled frustrated Ising spins take into account for frustrating effects like the geometrical hindrance. We show that in this model dynamical transitions and crossovers are related to static transitions. In particular, when disorder is present, as predicted and verified in SG, a dynamical transition between high-temperatures exponential to low-temperatures non-exponential correlation functions numerically coincides with the ordering temperature of the ferromagnetic regions, i.e. the Griffiths temperature $T_c(s)$, while a crossover between power law growth of correlation times to Arrhenius law occurs near a Potts transition at $T_p(s), Comment: 11 pages, 4 figures

We introduce a schematic non-linear diffusion model where density fluctuations induce a rich out of equilibrium dynamics. The properties of the model are studied by numerical simulations and analytically in a mean field approximation. At low temperatures and high densities we find a long off-equilibrium glassy region, where the system evolves out of an initially pinned state showing aging and a slow decay of the autocorrelation as an enhanced power law, along with strong spatial heterogeneities and violation of the fluctuation dissipation theorem., 4 pages, 2 figures

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = \phi_1(t)^{f(\beta)}{\cal{S}}(\beta)$, where the scaling variable is $\beta=\beta(\phi_1(t')/\phi_1(t))$ and $\phi_1(t')$, $\phi_1(t)$ two undetermined functions. The presence of a non constant exponent $f(\beta)$ signals the appearance of multiscaling properties in the dynamics., Comment: 6 pages, no figures

We numerically study the dynamical properties of fully frustrated models in 2 and 3 dimensions. The results obtained support the hypothesis that the percolation transition of the Kasteleyn-Fortuin clusters corresponds to the onset of stretched exponential autocorrelation functions in systems without disorder. This dynamical behavior may be due to the ``large scale'' effects of frustration, present below the percolation threshold. Moreover these results are consistent with the picture suggested by Campbell et al. in space of configurations., Comment: 8 pages, 11 figures, revised version

We study the properties of the q-state frustrated bond percolation model by a Monte Carlo "bond flip" dynamics, using an algorithm originally devised by Sweeny and suitably modified to treat the presence of frustration. We analyze the percolation transition of the model, and find that it falls in the universality class of the q/2-state ferromagnetic Potts model. We then investigate the bond flip dynamics of the model, and find that for temperatures lower than the percolation transition Tp the relaxation functions show a two step decay, reminiscent of the relaxation of glass forming liquids. The long time decay (alpha-relaxation) is well fitted for T, Comment: 10 pages, 19 figs, RevTeX

We study microscopic and macroscopic dynamical properties of a frustrated lattice gas, strictly related to usual spin glasses, showing the violation of Stokes-Einstein law. The glassy behaviors are analyzed and related with experimental results in glass former systems., 4 pages, to be published in Phys. Rev. E, Rapid Communication

The dynamical properties of the site frustrated percolation model are investigated and compared with those of glass forming liquids. When the density of the particles on the lattice becomes high enough, the dynamics of the model becomes very slow, due to geometrical constraints, and rearrangement on large scales is needed to allow relaxation. The autocorrelation functions, the specific volume for different cooling rates, and the mean square displacement are evaluated, and are found to exhibit glassy behavior., 8 pages, RevTeX, 11 figs