Search

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

By changing the control parameters, many physical systems reach a slow dynamics regime followed by an arrested or a quasi-arrested state. Examples, among others, are gels and glasses. In this paper, we discuss some experimental and theoretical results in polymer and colloidal systems, where gel and glass transitions interfere, and use models from Mode Coupling Theory (MCT) to illustrate the rich phenomenology observed. The continuous and the discontinuous transition lines, found in the MCT models, are considered suitable to describe respectively the gel and the glass transitions, so we suggest that the interplay between gel and glass may be interpreted in terms of the $F_{13}$ MCT model, clarifying also the origin of logarithmic decays often observed in such systems. In particular, the theoretical predictions of the MCT in the $F_{13}$ model are compared with Molecular Dynamics simulations in model systems for chemical gels and charged colloids.

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

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 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

Based on various results present in the literature, we elaborate a unifying cluster percolation approach, to interpret the dynamical arrest occurring in amorphous materials such as gels, glasses and granular materials. In the case of the sol-gel transition, this cluster approach predicts scaling laws relating the dynamical exponents to random percolation critical exponents. Interestingly, in mean-field such relations coincide with those predicted by the schematic continuous Mode Coupling Theory, known as model A. More appropriate to describe molecular glass transition is the schematic discontinuous Mode Coupling Theory known as model B. In this case a similar cluster approach and a diffusing defect mechanism predicts scaling laws, relating the dynamical exponents to static critical exponents of the bootstrap percolation. In finite dimensions a glass theory based on the Random First Order Transition suggests that the Mode Coupling Theory transition is only a crossover towards an ideal glass transition characterized by the divergence of cooperative rearranging regions. Interestingly, also this scenario can be mapped onto a mixed order percolation transition, where the order parameter jumps discontinuously at the transition, while the mean cluster size and the linear cluster dimension diverge. A similar mixed order percolation transition seems to apply also to the jamming transition.a#13

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

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

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"