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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

We investigate the glass and the jamming transitions of hard spheres in finite dimensions $d$, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite $d$. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent $\nu=2/d$, which we verify through finite size scaling, and standard critical exponents $\alpha = 0$, $\beta = 0$ and $\gamma = 2$ independent on $d$.

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 have performed a detailed analysis of the local dynamics and local energies of the equilibrium, paramagnetic phase of the d = 2 and d = 3 ±J Ising spin glass model. Here we discuss our recently reported observations l) that while the average flip rate and average energy decrease monotonically with decreasing temperature, both the flip rate and energy of an increasing fraction of spins increase as the glass transition is approached on cooling. These findings are consistent with recent experimental results for the frequency-dependent magnetic susceptibility of an insulating spin glass, which showed that the approach to the glass transition could be detected from the high frequency behavior. In an effort to better understand the effects of frustration as the glass transition is approached, and to elucidate recent claims of the presence and ramifications of dynamic heterogeneities significantly above the glass transition temperature Tg in glass-forming materials with self-induced frustration, 2 )- 7 ) we are currently exploring the relationship between microstructure and local dynamics in a variety of systems, including supercooled liquids with self-induced disorder 8 ) and paramagnets with random, quenched disorder. 1 ) In particular, we have recently performed a detailed Monte Carlo simulation study of the paramagnetic phase of the Ising spin glass to characterize the hetero­ geneities induced in this system by the quenched disorder, and to test the model for the emergence of fast processes recently reported in an experimental study of an Ising-like spin glass. 4 ) In the Ising spin glass model, exchange interactions Jij = ±J are fixed randomly to the edges of a lattice, and Ising spins with values

The structural arrest of a polymeric suspension might be driven by an increase of the cross-linker concentration, which drives the gel transition, as well as by an increase of the polymer density, which induces a glass transition. These dynamical continuous (gel) and discontinuous (glass) transitions might interfere, since the glass transition might occur within the gel phase, and the gel transition might be induced in a polymer suspension with glassy features. Here we study the interplay of these transitions by investigating via event-driven molecular dynamics simulation the relaxation dynamics of a polymeric suspension as a function of the cross-linker concentration and the monomer volume fraction. We show that the slow dynamics within the gel phase is characterized by a long sub-diffusive regime, which is due both to the crowding as well as to the presence of a percolating cluster. In this regime, the transition of structural arrest is found to occur either along the gel or along the glass line, depending on the length scale at which the dynamics is probed. Where the two lines meet there is no apparent sign of higher order dynamical singularity. Logarithmic behavior typical of A3 singularity appears inside the gel phase along the glass transition line. These findings seem to be related to the results of the mode coupling theory for the F13 schematic model.

The dynamical susceptibility has been introduced to characterize the dynamical heterogeneities in glass forming liquids. We have used it as a tool to investigate the slow dynamics of other disordered systems such as gels, granular media and spin glasses. We review here the results obtained via numerical simulations of different model systems. The comparative study of the behaviour of the dynamical susceptibility sheds some light on the significant differences in the complex slow dynamics of glasses, spin glasses, granular media, irreversible gels, and colloidal gels.

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 study the segregation process of a granular mixture of discs on an horizontally oscillating tray by realistic molecular dynamics simulations. As found in the experiments, we observe the initially disordered mixture to segregate via the formation of stripes perpendicular to the driving direction. The segregation process turns out to be the result of a dynamical instability very similar to the Kelvin–Helmholtz instability observed in fluid mechanics, and it is not due to the depletion potential, i.e., to the effective potential existing between two big particles in a bath of smaller ones, but rather to a dynamical process whose nature is discussed.

A system under gravity, made up of hard spheres with an internal degree of freedom, is studied on a 3d lattice under a Monte Carlo “tap” dynamics. A “jamming” transition similar to that found in real experiment is found. To understand the nature of such transition a simplified version of the model is also studied in a mean field approximation, using the statistical mechanics approach a la Edwards. A phase transition from a “fluid” to a “glassy” phase is found when crystallization is avoided. Interestingly, the nature of such a “glassy” phase turns out to be the same found in mean field models for glass formers.

We briefly review a Statistical Mechanics approach for the description of granular materials following the original ideas developed by Edwards. We show that Edwards’ assumptions works very well for a class of lattice models and we discuss some recent analytic results obtained in such a framework on their phase diagram, jamming transition and mixing/segregation properties.

A cell theory for glassforming liquids, amorphous solids and granular packings, is developed by combining geometrical properties of local packings with the ideas of inherent structures and free volume theory. We show that for hard-spheres the present theory reproduces well the equation of state, the approach to zero of the configurational entropy and the divergence of large relaxation times following both the Vogel–Tammann–Fulcher behavior and the Adam–Gibbs relation.

We present a novel theoretical approach to understanding the complex dynamics of glass-forming liquids, granular packings and amorphous solids. This theory, which is an elaboration of the free volume and inherent structure approaches, allows one to retrieve the thermodynamical properties of these systems from studies of geometrical and topological properties of local, static configurations alone. When applied to hard-sphere systems, the present theory reproduces with a good quantitative agreement the equation of state for the crystalline and the disordered glassy phases. Moreover, we find that, as the density approaches a critical value close to the random close-packing density, the configurational entropy approaches zero and the large relaxation time diverges according to the Vogel–Fulcher behaviour, following also the Adam–Gibbs relation.

In this paper we study the 3D frustrated lattice gas model in the quenched and annealed versions. In the first case, the dynamical non-linear susceptibility grows monotonically as a function of time, until reaching a plateau that corresponds to the static value. The static non-linear susceptibility diverges at some density, signaling the presence of a thermodynamical transition. In the annealed version, where the disorder is allowed to evolve in time with a suitable kinetic constraint, the thermodynamics of the model is trivial, and the static non-linear susceptibility does not show any singularity. Nevertheless, the model shows a maximum in the dynamical non-linear susceptibility at a characteristic value of the time. Approaching the density corresponding to the singularity of the quenched model, both the maximum and the characteristic time diverge. We conclude that the critical behavior of the dynamical susceptibility in the annealed model is related to the divergence of the static susceptibility in the quenched case. This suggests a similar mechanism also in supercooled glass-forming liquids, where an analogous behavior in the dynamical non-linear susceptibility is observed.

We consider the dynamics of supercooled fluids subject to a continuous quenching procedure, with cooling rate r = dT(t)/dt. The analysis is carried out analytically in the framework of a mean field schematic model recently introduced.1 We show the existence of a glass temperature Tg(r) below which the system falls out of equilibrium. Tg(r) approaches logarithmically in r the ideal glass temperature T0 = lim r→0Tg(r), where the relaxation time diverges á la Vogel-Fulcher, similarly to some experimental observations. Well above Tg(r) a simple fluid behavior is observed. As Tg is approached from above a characteristic wave vector kd divides an high momenta equilibrated region, where a fluid-like behavior is obeyed, from the non thermalized modes with k < kd, for which time translational invariance lacks. Below Tg the system is found in a globally off-equilibrium glassy state characterized by a logarithmic decay of the density fluctuations and aging. The two time correlator decays as an enhanced power law.

Clusters in frustrated systems are studied in the context of the frustrated percolation model. This model, which contains frustration and connectivity as an essential ingredient, exhibits a large degree of complexity in both static and dynamics. The bond version of the model maps on the spin glass model, while the site version can be applied to a large variety of frustrated systems such as glasses and granular materials.

The interplay between critical percolating clusters and critical points in physical systems and models is reviewed. The main emphasis is given to systems such as colloids and gels. Much information on the main mechanism leading to percolation in correlated systems can be obtained from the study of the Ising model. It is emphasized that different cluster definitions are necessary for studying different phenomena and that the possibility of experimentally detecting the percolation line is related to the cluster lifetime. Some results on the interplay between critical points and percolating clusters in fluids are also discussed.

We present a study of molecular dynamics at the sol-gel transition. Application of percolation and bond-fluctuation dynamics provides critical exponents for viscoelastic properties in a strong covalent gel and shows a complex non-exponential relaxation behaviour. The results are in good agreement with experimental findings and offer interesting pointers for discussions.

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

We review the basic ideas which have been developed to characterize geometrically the equilibrium phase transitions. This approach elucidates many concepts like propagation of correlations, upper critical dimensionality, breakdown of hyperscaling, strong universality, and other basic ideas in phase transitions. More recently the extension of the geometrical approach to frustrated systems like spin glasses has lead to the definition of a new geometrical model called frustrated percolation. Application of this model to complex systems such as glasses and granular materials is also briefly reviewed.

In the four-dimensional Edwards–Anderson ±J spin glasses, we observe that the quenched energies distribution from T=2.5 are similar to those observed for the equilibrium states at T=1.0. We show that although these states appear close there are subtle differences which are only seen when we try to quench the system from T=2.5 for a longer number of Monte Carlo steps. The T=2.5 states do not evolve to those seen for the states quenched from T=1.0. We try to identify regions responsible for the subtle differences.

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 sol-gel transition is studied introducing the bond fluctuation dynamics within the percolation model in order to investigate both static and dynamic properties. Computer simulations on a square lattice have shown that the static properties agree with the random percolation model and the self-diffusion coefficients vanish at the percolation threshold. From the self-diffusion coefficients the critical behaviour of the viscosity at the sol-gel transition is determined, giving an exponent .

A three-dimensional (3D) spin-glass model diluted with lattice gas variables is investigated and compared with glass-forming liquids. The spin variables which play the role of internal degrees of freedom exhibit strong fluctuations. While a critical length associated to these fluctuations diverges at the glass transition, where the diffusion coefficient is found to vanish, the density fluctuations do not show any critical behaviour.

We develop a Hamiltonian formalism for the frustrated percolation model. This is a cluster model which has recently received attention for its relevance to glassy systems and granular materials. The exact solution of the model on the frustrated hierarchical lattice of Mc Kay et al. exhibits a percolation transition with critical exponents of the ferromagnetic 1 2 - state Potts model and a spin glass transition characterized by chaotic renormalization group trajectories. Finally, we discuss the model in light of recent experiments.

The concepts of connectivity, localization, and frustration are explored in relation to glass formation in amorphous materials. First, the concept of eigenclusters to geometrically characterize correlations in amorphous materials is introduced, and discussed in detail for both the Ising ferromagnet and Ising spin glass models. Second, a new, glass-forming percolation model that contains frustration as the essential ingredient, and exhibits two percolation transitions, is discussed. This new model gives new insights into frustrated systems, and applications to the Ising spin glass model and other glass-forming systems are discussed. In particular, we propose the possibility that the occurrence of a percolation-type transition at temperatures above the glass transition temperature may be a general feature of glass-forming systems. The important role of computer simulations in probing the mechanism of glass formation is emphasized.

We report recent results of molecular dynamics simulations of frictional athermal particles at constant volume fraction and constant applied shear stress, focusing on a range of control parameters where the system first flows, but then jams after a time tjam. On decreasing the volume fraction, the mean jamming time diverges, while its sample fluctuations become so large that the jamming time probability distribution P(tjam) becomes a power-law. We obtain an insight on the origin of this phenomenology focusing on the flowing regime, which is characterized by the presence of a clear correlation between the shear velocity and the mean number of contacts per particles Z, whereby small velocities occur when Z acquires higher values., Comment: 10 pages, 7 figures

The purpose of this talk is to present a brief overview of our group's recent research into dynamic mechanisms of disorderly growth, an exciting new branch of condensed matter physics in which the methods and concepts of modern statistical mechanics are proving to be useful. Our strategy has been to focus on attempting to understand a single model system - diffusion limited aggregation (DLA). This philosophy was the guiding principle for years of research in phase transitions and critical phenomena. For example, by focusing on the Ising model, steady progress was made over a period of six decades and eventually led to understanding a wide range of critical point phenomena, since even systems for which the Ising model was not appropriate turned out to be described by variants of the Ising model (such as the XY and Heisenberg models). So also, we are optimistic that whatever we may learn in trying to "understand" DLA will lead to generic information helpful in understanding general aspects of dynamic mechanisms underlying disorderly growth.

Carlo computer simulations of spinodal decomposition to show that the model exhibits "pinning" of the structure factor, a behavior also seen in phase-separating polymer gels and binary alloys with impurities. The rate of strong bond formation depends on an entropic parameter 0, and we fInd both the pinned domain size and the crossover time between "normal" spinodal decomposition and the pinning scale with 0 as power laws with exponents that relate simply to the usual growth exponent. We propose a speci6c mechanism for pinning that permits the prediction of exact values for the pinning exponents. Finally, we discuss applications of the model to binary alloys with quenched disorder and polymer gels.

We study the dynamical behavior in chemical gelation, as the gelation threshold is approached from the sol phase. On the basis of the heterogeneous diffusion due to the cluster size distribution, as expected by the percolation theory, we predict the long time decay of the self-overlap as a power law in time t(-3/2). Moreover, under the hypothesis that the cluster diffusion coefficient decreases in size as a power law, s(-x), the fluctuation of the self-overlap, χ(4)(t), exhibits growth at short time as t((3-τ)/x), where τ is the cluster size distribution critical exponent. At longer times, χ(4)(t) decays as t(-3/2) while, at intermediate times, it reaches a maximum at time t*, which scales as s*(x), where s* is the size of the critical cluster. Finally, the value of the maximum χ(4)(t*) scales as the mean cluster size. The theoretical predictions are in agreement with molecular dynamic calculations in a model system, where spherical monomers are bonded by a finite extendable nonlinear elastic (FENE) potential.

We study the dynamical properties of a model for charged colloidal particles, performing molecular dynamics simulations and observing the behavior of bond persistence functions, self-intermediate scattering functions at different wave vectors, and mean-square displacements of the particles, in three different regimes of the volume fraction. At the lowest volume fraction the system displays properties very similar to those of a gelling system, which can be interpreted in terms of the distribution of cluster sizes, with a peak in the dynamical susceptibility at the lowest wave vector. At the highest volume fraction, a percolating network of bonds is always present, and the system is strongly reminiscent of strong glasses, with the maximum in the dynamical susceptibility increasing when the temperature is lowered, and an Arrhenius dependence of the relaxation times. At intermediate volume fractions, a complex behavior is found, where both the distribution of cluster sizes and the intercluster correlations due to crowding are important.

We review some recent results relevant to colloidal systems with competing interactions. In particular we report some findings concerning the pattern formation phenomena obtained in a φ4 theory. Some of the general features are also found in an atomistic model by means of a thermodynamic approach and molecular dynamics simulations. Finally this model is shown to exhibit a structural arrest in a disordered gel-like state, once the ordered state is avoided.

We study the dynamical heterogeneities along the attractive glass line in a model for charged colloids, where short-range attraction competes with long-range repulsion. We focus on the crossover from gel-like to glassy-like regime, where the system displays both features of chemical gels and of glassy systems. The former are due to long living clusters the latter to crowding effects, which both slow down the relaxation process. We show how to separate the two effects by looking at the fluctuation of the self Intermediate Scattering Function, χ 4(k,t), for different values of wave vector k. For small values of k, χ 4(k,t) detects the dynamical behavior at large length scale, where both cluster effects and crowding effects are present. On the other hand by increasing the value of k, χ 4(k,t) detects the dynamical behavior at small length scale where the cluster effects are suppressed and only the crowding effects dominate the dynamics.

Recent work showing evidence for multiscaling in large two dimensional DLA clusters is reviewed. A connection between multiscaling and multifractality is also shown resulting in a weak localization of the growth sites (δ-sites) in shells around the cluster seed.

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.

Systems of particles interacting via short-ranged repulsive forces are characterized by a jamming transition from a flowing to a disordered solid state, whose understanding is of great theoretical and practical relevance. The jamming phase diagram introduced by Liu and Nagel in 1998 provided a conceptual picture from which to investigate this transition, suggesting that the shear stress might play a role analogous to that of temperature in the jamming phenomenology. Here we highlight recent works which suggest qualitative changes in the shape of the diagram.

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

We describe the sol-gel transition by introducing an order parameter, defined as the average of local variables, and its fluctuations. It can be shown that these quantities are related to percolation quantities, but in principle they can be measured without resorting to connectivity properties. In this framework it appears that the dynamical transition associated with gelation is a real thermodynamic transition, as happens in spin glasses. The strong analogies between the sol-gel transition and the spin glass transition are also discussed.

Exact relations between cluster properties and thermodynamical properties are obtained for an Ising spin glass. The size of the clusters diverges at a temperature higher than the spin-glass transition. The clusters represent fluctuations that interfere with each other giving rise to net correlations of much shorter size than the typical cluster radius. A frustrated-percolation model is introduced that is related to the Ising spin glass as standard percolation is related to the Ising model.

A novel dynamical scaling characterized by infinitely-many growth exponents is presented. This new behavior is manifested in the time-dependent pair correlation function and therefore is amenable to direct experimental observation. An exact analytical solution on the time-dependent Ginzburg-Landau model is obtained in the large- N limit for a quench at zero temperature, which exhibits such multiscaling behavior. This new form of behavior reflects a morphological pattern in the growing domains and is expected in other growth phenomena, as indicated by preliminary analysis on DLA clusters. A connection between multiscaling and multifractality is discussed.

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

We review recent results about the segregation process of a granular mixture of disks on an horizontally oscillating tray. In this condition an initially disordered mixture first segregates via the formation of stripes perpendicular to the driving direction; then stripes merge in a coarsening process. We discuss quantitatively both the short-time and the long-time dynamics of the system, and the dependence of the observed phenomenology on the frequency and amplitude of oscillation of the tray. The same system is also investigated when, instead of being disordered, is initially prepared in two stripes parallel to the driving direction. In this condition the interface between the two stripes manifests an instability which again leads to the formation of stripes perpendicular to the driving direction. Finally, we shortly review the mechanism which have been proposed in order to explain the observed segregation process.

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 analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, 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 strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales., Comment: Final version, accepted for publication in Phys. Rev. Lett

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 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

We review some results on the dynamics of gelation phenomena, obtained via a lattice model and via molecular dynamics using a DLVO potential. This study allowed us to make a connection between classical gelation and the phenomenology of colloidal systems, suggesting that gelation phenomena in attractive colloids at low temperature and low volume fraction can be described in terms of a two-line scenario.

The basic cluster formalism which maps the Ising model into a correlated percolation model will be discussed. More recently the extension of the cluster approach to frustrated systems, like spin glasses, has lead to the definition of a new geometrical model, called frustrated percolation. The properties of this model will be reviewed.