Relation between statics and dynamics in the quench of the Ising model to below the critical point.

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 ensure 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 from each 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.

Condensation of fluctuations in the Ising model: A transition without spontaneous symmetry breaking.

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 either ergodicity or 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 T_{c}. The argument is developed exactly in the d=1 case and numerically in the d=2 case.

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres.

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 ν = 2/d, which we verify through finite size scaling, and standard critical exponents α = 0, ß = 0 and γ = 2 independent on d.

Force percolation transition of jammed granular systems.

The mechanical and transport properties of jammed materials originate from an underlying percolating 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.

Scaling and universality in glass transition.

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 〈q(t)〉 and the dynamical susceptibility 〈q(2)(t)〉 - 〈q(t)〉(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 dc = 8.

Particle jumps in structural glasses.

Particles in structural glasses rattle around temporary equilibrium positions, 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 particle 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.

Spatial correlations of elementary relaxation events in glass-forming liquids.

The dynamical facilitation scenario, by which localized relaxation events promote nearby relaxation events in an avalanche 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 numerical simulations 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 characteristics of this avalanche change upon 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 triggers more relaxation events.

Dynamic phase coexistence in glass-forming liquids.

One of the most controversial hypotheses for explaining the heterogeneous dynamics of glasses postulates the temporary coexistence of two phases characterized by a high and by a low diffusivity. In this scenario, two phases with different diffusivities coexist for a time of the order of the relaxation time and mix afterwards. Unfortunately, it is difficult to measure the single-particle diffusivities to test this hypothesis. Indeed, although the non-Gaussian shape of the van-Hove distribution suggests the transient existence of a diffusivity distribution, it is not possible to infer from this quantity whether two or more dynamical phases coexist. Here we provide the first direct observation of the dynamical coexistence of two phases with different diffusivities, by showing that in the deeply supercooled regime the distribution of the single-particle diffusivities acquires a transient bimodal shape. We relate this distribution to the heterogeneity of the dynamics and to the breakdown of the Stokes-Einstein relation, and we show that the coexistence of two dynamical phases occurs up to a timescale growing faster than the relaxation time on cooling, for some of the considered models. Our work offers a basis for rationalizing the dynamics of supercooled liquids and for relating their structural and dynamical properties.

Percolation approach to glassy dynamics with continuously broken ergodicity.

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 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.

From cage-jump motion to macroscopic diffusion in supercooled liquids.

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, and show that single-particle jumps are the irreversible events leading to the relaxation of the system. This allows us to evaluate the diffusion constant on the time-scale of the jump duration, which is small and temperature independent, i.e. well before the system enters the diffusive regime. The prediction is obtained by analyzing the particle trajectories via a parameter-free algorithm.

Dynamical arrest: interplay of glass and gel transitions.

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.

Monte Carlo renormalization-group analysis of percolation.

We describe a Monte Carlo renormalization group approach to the calculation of critical behavior for percolation models. This approach can be utilized to determine the renormalized bond probabilities and the values of the critical exponents. We illustrate the method for two-dimensional bond percolation, but the method is also applicable to other percolation models and other dimensions.

Jamming phase diagram for frictional particles.

We investigate the jamming transition of frictional particulate systems via discrete element simulations, reporting the existence of new regimes, which are conveniently described in a jamming phase diagram with axes density, shear stress, and friction coefficient. The resulting jammed states are characterized by different mechanical and structural properties and appear not to be "fragile" as speculated. In particular, we find a regime, characterized by extremely long processes, with a diverging time scale, whereby a suspension first flows but then suddenly jams. We link this sudden jamming transition to the presence of impeded dilatancy.

Dynamical correlation length and relaxation processes in a glass former.

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.

Relaxation process and dynamical heterogeneities in chemical gels: critical behavior of self-overlap and its fluctuation.

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.

Clusters in colloidal systems.

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.

Aggregation of fibrils and plaques in amyloid molecular systems.

Amyloidlike proteins form highly organized aggregates, such as fibrils and plaques, preceded by the assembly of a wide range of unstructured oligomers and protofibrils. Despite their importance in a number of human neurodegenerative diseases, a comprehensive understanding of their kinetics and thermodynamics is still missing. We investigate, by computer simulations, a realistic model of amyloid molecules interacting via the experimentally determined Derjaguin-Landau-Verwey-Overbeek potential and derive its phase diagram. We show that fibrils and plaques, along with their precursors, correspond to different equilibrium and metastable thermodynamics phases and discuss the dynamical mechanisms leading to the nucleation and self-assembly of large scale structures.

Jamming at zero temperature, zero friction, and finite applied shear stress.

Shear stress, as temperature, induces particle motion, and affects the jamming transition from a fluid to a disordered solid state. Here, we show that at finite shear stress, the jamming transition is characterized by the presence of hysteresis, as in a given range of control parameters a flowing or a jammed state can be found, depending on whether the system is prepared coming from the fluid or the jammed phase. At small shear stress, where the hysteresis is negligible, the jamming transition has a mixed first-order second-order character close to that found at the glass transition of thermal systems, with discontinuities in the asymptotic values of two time quantities such as the self-intermediate scattering function.

Random very loose packings.

We measure the number Omega(phi) of mechanically stable states of volume fraction phi of a granular assembly under gravity. The granular entropy S(phi)=logOmega(phi) vanishes both at high density, at phi approximately equal to phi_rcp, and a low density, at phi approximately equal to phi_rvlp, where phi_rvlp is a new lower bound we call random very loose pack. phi_rlp is the volume fraction where the entropy is maximal. These findings allow for a clear explanation of compaction experiments and provide the first first-principle definition of the random loose volume fraction. In the context of the statistical mechanics approach to static granular materials, states with phi

Flow, ordering, and jamming of sheared granular suspensions.

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 or 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.