Renormalization group study of a kinetically constrained model for strong glasses

Whitelam, Stephen; Berthier, Ludovic; Garrahan, Juan P.

doi:10.1103/physreve.71.026128

Cited by 55 publications

(69 citation statements)

References 76 publications

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“…The one-spin facilitated FA model has been studied numerically and analytically in various spatial dimensions in much detail [13,14,28,47,48,54,58,59,60]. These studies have shown that the model exhibits dynamic heterogeneity and large spontaneous fluctuations of the twotime dynamics, although relaxation timescales grow only in an Arrhenius fashion as temperature is decreased,…”

Section: B Results For 1-spin Facilitated Fa Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

Berthier

Biroli

Bouchaud

et al. 2007

The Journal of Chemical Physics

193

297

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We study in detail the predictions of various theoretical approaches, in particular mode-coupling theory (MCT) and kinetically constrained models (KCMs), concerning the time, temperature, and wavevector dependence of multi-point correlation functions that quantify the strength of both induced and spontaneous dynamical fluctuations. We also discuss the precise predictions of MCT concerning the statistical ensemble and microscopic dynamics dependence of these multi-point correlation functions. These predictions are compared to simulations of model fragile and strong glass-forming liquids. Overall, MCT fares quite well in the fragile case, in particular explaining the observed crucial role of the statistical ensemble and microscopic dynamics, while MCT predictions do not seem to hold in the strong case. KCMs provide a simplified framework for understanding how these multi-point correlation functions may encode dynamic correlations in glassy materials. However, our analysis highlights important unresolved questions concerning the application of KCMs to supercooled liquids.

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Section: B Results For 1-spin Facilitated Fa Modelsmentioning

confidence: 99%

“…Therefore it shows a peak, χ ⋆ 4 (T ) = χ 4 (t ∼ τ α ), whose position shifts to larger times and whose height increases when temperature decreases. One finds dynamic scaling [13,47,58],…”

Section: B Results For 1-spin Facilitated Fa Modelsmentioning

confidence: 99%

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

Berthier

Biroli

Bouchaud

et al. 2007

The Journal of Chemical Physics

193

297

View full text Add to dashboard Cite

show abstract

“…For estimates of the dynamic correlation lengths based on experimental studies, see [5]. For recent simulation and theoretical studies of dynamic heterogeneity, see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

mentioning

confidence: 99%

“…One approach to the theoretical understanding of dynamic heterogeneity is based on the use of kinetically constrained lattice models [4,11,12,[15][16][17][18][19][20]23,[25][26][27]. Another approach is based on generalizations [7,22] of the mode-coupling theory of Götze [28].…”

mentioning

confidence: 99%

Scaling Analysis of Dynamic Heterogeneity in a Supercooled Lennard-Jones Liquid

Stein

Andersen

2008

Phys. Rev. Lett.

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We have performed molecular dynamics computer simulations of a dense Lennard-Jones liquid mixture to study dynamic heterogeneity from normal liquid temperatures down to a supercooled temperature 15% above the previously identified mode-coupling temperature Tc of the model. A temperature-dependent correlation length associated with the correlation function of mobility fluctuations is calculated. The results are used to test two sets of scaling hypotheses for the dynamic heterogeneity. The results are in close agreement with the inhomogeneous mode-coupling theory of Biroli et al. [Phys. Rev. Lett. 97, 195701 (2006)] for both the alpha and beta relaxation regimes. Comparison with results for kinetically constrained models suggest that the Lennard-Jones mixture studied is more similar to models of fragile liquids than models of very strong liquids.

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“…In various model systems of the supercooled liquids, the scaling law has been found for the dynamic length and time scales. 36,[58][59][60][61] It is noted that these kinds of relations are originally found in the critical behavior of phase transitions. In our ionic liquid model system, a similar power law relation is discovered.…”

Section: Scaling Lawsmentioning

confidence: 99%

Heterogeneous dynamics and its length scale in simple ionic liquid models: a computational study

Kim

Park

Jung

2016

Phys. Chem. Chem. Phys.

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We numerically investigate the dynamic heterogeneity and its length scale found in the coarse-grained ionic liquid model systems. In our ionic liquid model systems, cations are modeled as dimers with positive charge, while anions are modeled as monomers with negative charge, respectively. To study the effect of the charge distributions on the cations, two ionic liquid models with different charge distributions are used and the model with neutral charge is also considered as a counterpart. To reveal the heterogeneous dynamics in the model systems, we examine spatial distributions of displacement and time distributions of exchange and persistence times. All the models show significant increase of the dynamic heterogeneity as the temperature is lowered. The dynamic heterogeneity is quantified via the well-known four-point susceptibility, χ 4 (t), which measures the fluctuation of a time correlation function.The dynamic correlation length is calculated by fitting the dynamic structure factor, S 4 (k, t), with Ornstein-Zernike form at the time scale at which the dynamic heterogeneity reaches the maximum value. Obtained time and length scales exhibit a power law relation at the low temperatures, similar to various supercooled liquid models.Especially, the charged model systems show unusual crossover behaviors which are not observed in the uncharged model system. We ascribe the crossover behavior to the enhanced cage effect caused by charges on the particles.

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Renormalization group study of a kinetically constrained model for strong glasses

Cited by 55 publications

References 76 publications

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

Spontaneous and induced dynamic correlations in glass formers. II. Model calculations and comparison to numerical simulations

Scaling Analysis of Dynamic Heterogeneity in a Supercooled Lennard-Jones Liquid

Heterogeneous dynamics and its length scale in simple ionic liquid models: a computational study

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