Kob-Andersen model: A nonstandard mechanism for the glassy transition

Franz, Silvio; Mulet, Roberto; Parisi, Giorgio

doi:10.1103/physreve.65.021506

Cited by 41 publications

(56 citation statements)

References 24 publications

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“…Nevertheless in [29,30] it has been proven that the infinite volume process is always ergodic at any finite density, namely p c = 1. This contradicts previous claims [15,17,26] on the existence of a finite critical density.…”

Section: Definition 11 a Model Is Said To Be Non-cooperative If Itscontrasting

confidence: 54%

“…Therefore it is possible that the process undergoes a transition from an ergodic to a non ergodic regime when the particle density p crosses a critical value p c ∈ (0, 1). This has indeed been conjectured for some cooperative models [15,17,26]. The same issue for non-cooperative models is trivially solved for any p < 1 because of the µ p -almost sure existence of the mobile cluster.…”

Section: Definition 11 a Model Is Said To Be Non-cooperative If Itsmentioning

confidence: 64%

“…We mainly focus on the cooperative model which has been most studied in physics literature, the so called Kob Andersen (KA) model, which was introduced in [15] and subsequently studied in several works [3,17,26,25,29,30,18,21].…”

Section: Definition 11 a Model Is Said To Be Non-cooperative If Itsmentioning

confidence: 99%

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Kinetically Constrained Lattice Gases

Cancrini

Martinelli

Roberto³

et al. 2010

Commun. Math. Phys.

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ABSTRACT. Kinetically constrained lattice gases (KCLG) are interacting particle systems which show some of the key features of the liquid/glass transition and, more generally, of glassy dynamics. Their distintictive signature is the following: i) reversibility w.r.t. product i.i.d. Bernoulli measure at any particle density and ii) vanishing of the exchange rate across any edge unless the particle configuration around the edge satisfies a proper constraint besides hard core. Because of degeneracy of the exchange rates the models can show anomalous time decay in the relaxation process w.r.t. the usual high temperature lattice gas models particularily in the so called cooperative case, when the vacancies have to collectively cooperate in order for the particles to move through the systems. Here we focus on the Kob-Andersen (KA) model, a cooperative example widely analyzed in the physics literature, both in a finite box with particle reservoirs at the boundary and on the infinite lattice. In two dimensions (but our techniques extend to any dimension) we prove a diffusive scaling O(L 2 ) (apart from logarithmic corrections) of the relaxation time in a finite box of linear size L. We then use the above result to prove a diffusive decay 1/t (again apart from logarithmic corrections) of the spin-spin time autocorrelation function at any particle density, a result that has been sometimes questioned on the basis of numerical simulations. The techniques that we devise, based on a novel combination of renormalization and comparison with a long-range Glauber type constrained model, are robust enough to easily cover other choices of the kinetic constraints.

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Section: Definition 11 a Model Is Said To Be Non-cooperative If Itscontrasting

confidence: 54%

Section: Definition 11 a Model Is Said To Be Non-cooperative If Itsmentioning

confidence: 64%

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Kinetically Constrained Lattice Gases

Cancrini

Martinelli

Roberto³

et al. 2010

Commun. Math. Phys.

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“…This is of relevance for the understanding of the underlying mechanisms, also in view of similar behaviours exhibited by other kinds of models whose features can however be traced back to different origin [47].…”

Section: Discussionmentioning

confidence: 99%

Lattice models of disorder with order

Petri¹

2003

Braz. J. Phys.

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This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states. I IntroductionIn recent years, there is growing interest in systems commonly found in disordered structural configurations such as glasses and dense granulates. Clearly different in many respects, these two classes of materials share in common the property of displaying stable states which are very far from what would be expected from equilibrium considerations [1,2]. As a consequence of this property other features emerge, like slow relaxation and response functions.Models of disorder are generally based on the presence of quenched, or a priori, disorder which takes the system far from ordered configurations. Only recently it has been observed that lattice models capable of ordering can also well reproduce many properties of disordered systems. On the other hand glass formers in nature usually have crystalline states as ground states, but this does not prevent them from being frequently found in some glassy state. The situation for a granular system is in general different, insofar as irregular grains inhibit the evolution of ordered states. Nevertheless even in the case of identical beads it is practically impossible to arrange them into an ordered fashion merely by supplying the energy to them.The aim of this paper is to briefly review some lattice models employed in the description of the slow dynamics of glasses and dense granular matter, which do not possess any a priori disorder nor long range interactions. We shall not discuss in detail the models, but just recall some of the main results, addressing the interested reader to the bibliography. More attention will be drawn to some recent observations regarding the condition for the emergence of glassy phases in some models of this kind.The paper is structured as follows: in Section II exclusion models and hard particle models are briefly introduced together with their employment in irreversible dynamics; Section III is devoted to their use in the description of dense granular matter and related results; Section IV describes spin models which have been recently shown to exhibit glassy states and associated slow dynamics; finally in Sec. V some new ideas are illustrated on when and why glassy states are generated in the place of crystalline states in some lattice models. II Exclusion and hard particle modelsFlory [3] modeled the irreversible deposition of dimers on a one-dimensional surface by the random sequential adsorption (RSA) of particles on a lattice. In this model, particles are placed one at time at randomly chosen positions of a ...

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“…In particular, this issue was recently investigated in the KA model [49,55] without gravity using fourth-order correlation functions [45,46]. In Ref.…”

Section: Heterogeneitiesmentioning

confidence: 99%

Heterogeneities in aging models of granular compaction

Arenzon¹

2006

Braz. J. Phys.

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Kinetically constrained models (KCM) are systems with trivial thermodynamics but often complex dynamical behavior due to constraints on the accessible paths followed by the system. Exploring these properties, the KobAndersen (KA) model was introduced to study the slow dynamics of glass forming liquids and later extended to granular materials. In this last context, we present new results on the heterogeneous character of both in and out of equilibrium dynamics, further stretching the granular-glass analogy.

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Kob-Andersen model: A nonstandard mechanism for the glassy transition

Cited by 41 publications

References 24 publications

Kinetically Constrained Lattice Gases

Kinetically Constrained Lattice Gases

Lattice models of disorder with order

Heterogeneities in aging models of granular compaction

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