Kinetically constrained models

Garrahan, Juan P.; Sollich, Peter; Toninelli, Cristina

doi:10.1093/acprof:oso/9780199691470.003.0010

Cited by 94 publications

(116 citation statements)

References 18 publications

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“…[12] and references therein), its role in the dynamics is debated. Alternative theories instead propose that the increase of τ α stems from growing barriers to the elementary rearrangements required to explore the landscape [13][14][15][16][17]. Such barriers effectively add a term to the activation energy E el = c 1 (T ).…”

Section: -Dmentioning

confidence: 99%

Does a Growing Static Length Scale Control the Glass Transition?

Wyart

Cates²

2017

Phys. Rev. Lett.

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Several theories of the glass transition propose that the structural relaxation time τα is controlled by a growing static length scale ξ that is determined by the free energy landscape but not by the local dynamical rules governing its exploration. We argue, based on recent simulations using particle-radius-swap dynamics, that only a modest factor in the increase in τα on approach to the glass transition may stem from the growth of a static length, with a vastly larger contribution attributable instead to a slowdown of local dynamics. This reinforces arguments that we base on the observed strong coupling of particle diffusion and density fluctuations in real glasses.PACS numbers: 64.70. Pf, When a liquid is cooled sufficiently rapidly to avoid crystallization, its viscosity η increases. In general, η ≃ Gτ α , where G is the (plateau) shear modulus and τ α characterizes the relaxation time of density fluctuations. As the temperature T is lowered, G evolves mildly but τ α increases by about 15 order of magnitude [1] until, at the transition temperature T G , it becomes too large to measure experimentally. The liquid then becomes a glass, and falls out of equilibrium. Near the glass transition, the diffusion of a tagged particle also becomes very slow. The characteristic time τ D over which a particle diffuses its own radius increases, albeit not as much as τ α . The decoupling of these two quantities (referred to as the Stokes-Einstein breakdown) is significant, but comparatively mild: the ratio S = τ α /τ D is increased by only a few orders of magnitude at T G [2,3].The dependence of τ α on T is used to classify glassy liquids [4]. Writing τ α = τ 0 exp(E/k B T ) where τ 0 is a vibrational time scale (in the picosecond range) and E some activation energy, one finds that E is constant in some liquids, called strong, but increases up to a factor 5 under cooling in other liquids, called fragile. Fragility is best shown in the 'Angell plot' of log(τ α ) vs. T G /T [4], which is linear for strong liquids but highly curved for fragile ones. Quantitatively, fragility is defined as There are competing explanations of the increase in the activation energy E in fragile liquids, which occurs with no obvious change of static structure [5]. Several theories, including the Adam-Gibbs scenario [6], Random First Order Theory (RFOT) [7][8][9], and those involving locally favored structures [10,11], posit that the increase in E stems from the growth of a purely static length scale ξ, characterizing some 'hidden order' in the many-body free-energy landscape that is not captured by traditional probes of static structure such as pair correlations.In particular, in modern interpretations of RFOT [7,8], ξ is a 'point-to-set' correlation length set by the minimum scale on which alternative packings are available to a patch of fluid whose environment is held frozen. Shorter scale motions do cross local barriers, but cannot discover a new pattern for the density which keeps returning to its initial state. In this view, regardless of how r...

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Section: -Dmentioning

confidence: 99%

Does a Growing Static Length Scale Control the Glass Transition?

Wyart

Cates²

2017

Phys. Rev. Lett.

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“…two-or more times correlations) share common features with generic glassy phenomena (see [26,27] for reviews on KCMs). They lend themselves rather easily for the study of their activity K, and for the analysis of the results.…”

Section: Fluctuations Of Dynamical Activitymentioning

confidence: 99%

Simulating Rare Events in Dynamical Processes

et al. 2011

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Atypical, rare trajectories of dynamical systems are important: they are often the paths for chemical reactions, the haven of (relative) stability of planetary systems, the rogue waves that are detected in oil platforms, the structures that are responsible for intermittency in a turbulent liquid, the active regions that allow a supercooled liquid to flow... Simulating them in an efficient, accelerated way, is in fact quite simple.In this paper we review a computational technique to study such rare events in both stochastic and Hamiltonian systems. The method is based on the evolution of a family of copies of the system which are replicated or killed in such a way as to favor the realization of the atypical trajectories. We illustrate this with various examples.

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“…The existence of these critical points is a crucial prediction of the thermodynamic mean field approach. On the contrary, in purely dynamic theories of glassyness [23] and in exactly solvable kinetically constrained models [24] (such as e.g.…”

Section: Introductionmentioning

confidence: 99%

Universality classes of critical points in constrained glasses

Franz

Parisi

2013

J. Stat. Mech.

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We analyze critical points that can be induced in glassy systems by the presence of constraints.These critical points are predicted by the Mean Field Thermodynamic approach and they are precursors of the standard glass transition in absence of constraints. Through a deep analysis of the soft modes appearing in the replica field theory we can establish the universality class of these points. In the case of the "annealed potential" of a symmetric coupling between two copies of the system, the critical point is in the Ising universality class. More interestingly, is the case of the "quenched potential" where the a single copy is coupled with an equilibrium reference configuration, or the "pinned particle" case where a fraction of particles is frozen in fixed positions. In these cases we find the Random Field Ising Model (RFIM) universality class. The effective random field is a "self-generated" disorder that reflects the random choice of the reference configuration. The RFIM representation of the critical theory predicts non-trivial relations governing the leading singular behavior of relevant correlation functions, that can be tested in numerical simulations.

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Kinetically constrained models

Cited by 94 publications

References 18 publications

Does a Growing Static Length Scale Control the Glass Transition?

Does a Growing Static Length Scale Control the Glass Transition?

Simulating Rare Events in Dynamical Processes

Universality classes of critical points in constrained glasses

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