The origin of glassy dynamics in the 2D facilitated kinetic Ising model

Butler, S. T.; Harrowell, Peter

doi:10.1063/1.461768

Cited by 104 publications

(106 citation statements)

References 24 publications

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“…[43][44][45][46] as experimental studies, and Refs. [17,18,42,[47][48][49][50][51][52][53] as numerical observations, and Refs. [19-21, 34-36, 54-57] as theoretical studies.…”

Section: Discussionmentioning

confidence: 99%

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

Iwata

Sasa

2010

Phys. Rev. E

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A Langevin equation whose deterministic part undergoes a saddle-node bifurcation is investigated theoretically. It is found that statistical properties of relaxation trajectories in this system exhibit divergent behaviors near a saddle-node bifurcation point in the weak-noise limit, while the final value of the deterministic solution changes discontinuously at the point. A systematic formulation for analyzing a path probability measure is constructed on the basis of a singular perturbation method. In this formulation, the critical nature turns out to originate from the neutrality of exiting time from a saddle-point. The theoretical calculation explains results of numerical simulations.

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“…[43][44][45][46] as experimental studies, and Refs. [17,18,42,[47][48][49][50][51][52][53] as numerical observations, and Refs. [19-21, 34-36, 54-57] as theoretical studies.…”

Section: Discussionmentioning

confidence: 99%

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

Iwata

Sasa

2010

Phys. Rev. E

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“…A more direct analysis of heterogeneities in the 2, 2-SFM was given by Butler and Harrowell [93]. They started the system from a random equilibrium configuration and then recorded for each spin how often it flipped within a time interval t. Obviously (if the system is large enough for reducibility effects to be negligible) then all spins should eventually flip infinitely often as t → ∞.…”

Section: Dynamical Lengthscales Cooperativity and Heterogeneitiesmentioning

confidence: 99%

“…For larger spatial dimension, d = 3, simulations of the 2, 3-SFM [266] found agreement with the theory of [74] over a broader range of c, as expected, although again there was no evidence of an actual dynamical transition. Butler and Harrowell [93,94] also obtained relaxation times for the 2, 2-SFM from simulations of the persistence function (see Sec. 5.3 below), finding the expected superactivated temperature-dependence.…”

Section: Relaxation Timescales and Dynamical Transitionsmentioning

confidence: 99%

Glassy dynamics of kinetically constrained models

Ritort

Sollich

2003

Advances in Physics

751

1,055

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We review the use of kinetically constrained models (KCMs) for the study of dynamics in glassy systems. The characteristic feature of KCMs is that they have trivial, often non-interacting, equilibrium behaviour but interesting slow dynamics due to restrictions on the allowed transitions between configurations. The basic question which KCMs ask is therefore how much glassy physics can be understood without an underlying "equilibrium glass transition". After a brief review of glassy phenomenology, we describe the main model classes, which include spin-facilitated (Ising) models, constrained lattice gases, models inspired by cellular structures such as soap froths, models obtained via mappings from interacting systems without constraints, and finally related models such as urn, oscillator, tiling and needle models. We then describe the broad range of techniques that have been applied to KCMs, including exact solutions, adiabatic approximations, projection and mode-coupling techniques, diagrammatic approaches and mappings to quantum systems or effective models. Finally, we give a survey of the known results for the dynamics of KCMs both in and out of equilibrium, including topics such as relaxation time divergences and dynamical transitions, nonlinear relaxation, aging and effective temperatures, cooperativity and dynamical heterogeneities, and finally non-equilibrium stationary states generated by external driving. We conclude with a discussion of open questions and possibilities for future work.

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“…In real glasses both effects are likely to be present. While most studies on the glass state have focused for a long time on the latter class of models, more attention is paid to the fact that the former mechanism is also of importance, especially since the works of Harrowell [4] on spatio-temporal heterogeneities. These heterogeneities are also of great interest for experimentalists, since they have been identified in several glassy systems [5].…”

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confidence: 99%

Spatial correlations in the relaxation of the Kob-Andersen model

Marinari¹,

Pitard²

2005

Europhys. Lett.

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PACS. 64.70.Pf -Glass transitions. PACS. 05.50.+q -Lattice theory and statistics. PACS. 61.20.Lc -Time-dependent properties of liquid structure; relaxation.Abstract. -We describe spatio-temporal correlations and heterogeneities in a kinetically constrained glassy model, the Kob-Andersen model. The kinetic constraints of the model alone induce the existence of dynamic correlation lengths, that increase as the density ρ increases, in a way compatible with a double-exponential law. We characterize in detail the trapping time correlation length, the cooperativity length, and the distribution of persistent clusters of particles. This last quantity is related to the typical size of blocked clusters that slow down the dynamics for a given density.Glassy dynamics in kinetically constrained systems has been a subject of wide interest during the last years [1]. It indeed includes a large class of models of particles constrained by dynamical rules where the relaxation is slowed down when the density of particles increases or the temperature decreases, sharing similarities (though with a number of differences) with spin-glass models or glass models [2] when the temperature is decreased. In the former class, slowing down of the dynamics can be understood as a consequence of steric effects, that make certain moves of particles impossible because of an effective high local density, putting strong constraints on the number of allowed paths between configurations [3]; whereas for the latter class, frustration and/or disorder in the interactions produces a slow time relaxation. In real glasses both effects are likely to be present. While most studies on the glass state have focused for a long time on the latter class of models, more attention is paid to the fact that the former mechanism is also of importance, especially since the works of Harrowell [4] on spatio-temporal heterogeneities. These heterogeneities are also of great interest for experimentalists, since they have been identified in several glassy systems [5].In this paper we will focus on the numerical study of the Kob-Andersen (KA) model [6]. In this 3-dimensional model of lattice gas on a cubic lattice, a particle can hop to one of its empty nearest neighbor sites only if it has strictly less than m occupied nearest-neighbor sites, and if after the hop it will also have less than m occupied nearest-neighbor sites (which ensures detailed balance). In the original study of the KA model, the value of m is chosen c EDP Sciences

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The origin of glassy dynamics in the 2D facilitated kinetic Ising model

Cited by 104 publications

References 24 publications

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

Theoretical analysis for critical fluctuations of relaxation trajectory near a saddle-node bifurcation

Glassy dynamics of kinetically constrained models

Spatial correlations in the relaxation of the Kob-Andersen model

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