Critical test of the mode-coupling theory of the glass transition

Berthier, Ludovic; Tarjus, Gilles

doi:10.1103/physreve.82.031502

Cited by 84 publications

(161 citation statements)

References 36 publications

Supporting

Mentioning

138

Contrasting

Order By: Relevance

“…Thus, for potentials having the same g liq (r) the theory will predict the same dynamical transition point. It has been shown in [89] that for some potentials this is not correct. This finding suggests that three-body, and higher order, liquid correlations might play an important role in glassy behavior for some systems.…”

Section: Discussionmentioning

confidence: 99%

Quantitative approximation schemes for glasses

Mangeat

Zamponi

2016

Phys. Rev. E

View full text Add to dashboard Cite

By means of a systematic expansion around the infinite-dimensional solution, we obtain an approximation scheme to compute properties of glasses in low dimensions. The resulting equations take as input the thermodynamic and structural properties of the equilibrium liquid, and from this they allow one to compute properties of the glass. They are therefore similar in spirit to the Mode-Coupling approximation scheme. Our scheme becomes exact, by construction, in dimension d → ∞ and it can be improved systematically by adding more terms in the expansion. ContentsI. Introduction A. The exact solution of infinite-dimensional glassy hard spheres B. Extension to finite dimension: state of the art C. Aim and structure of this paper II. Derivation of the equations A. The variational problem B. "Small cage" expansion C. Determination of G(r), and the final set of equations D. Discussion III. Connections with previous work A. Mézard-Parisi 1999 B. Parisi-Zamponi 2005 C. Berthier-Jacquin-Zamponi 2011 IV. Extracting physical quantities from the replicated free energy A. A convenient expression of q m,A (r) B. The equation for A and the complexity C. The equilibrium transition densities: dynamical transition and Kauzmann transition D. The jamming line E. Correlation functions and non-ergodicity factor V. Numerical methods A. Integral equations of liquid theory B. Discrete Fourier transformation C. Algorithm for g liq D. More accurate expressions for three-dimensional hard spheres E. Non-ergodicity factor F. Summary VI. Results: hard spheres A. HNC and PY results as a function of dimension B. Three dimensional results: thermodynamics C. Three dimensional results: non-ergodicity factor VII. Conclusions2. The dynamical transition density [8,12], at which the liquid phase becomes infinitely viscous and ergodicity is broken by the emergence of many metastable states. This transition is similar to the one of Mode-Coupling Theory (MCT) [23] and is thus characterized by MCT critical dynamical scaling, controlled by the so-called MCT parameter λ that can be also computed [8,12]. The Kauzmann transition [6], where the number of metastable states becomes sub-exponential, giving rise to an "entropy crisis" and a second order equilibrium phase transition.4. The Gardner transition line, that separates a region where glass basins are stable from a region where they are broken in a complex structure of metabasins [8,10,11].5. The density region where jammed packings exist (also known as "jamming line" or "J-line" [6,24,25]), which is delimited by the threshold density and the glass close packing density [6].6. The equation of state of glassy states, computed by compression and decompression of equilibrium glasses [11].7. The response of the glass state to a shear strain [11,26]. 8. The long time limit of the mean square displacement in the glass (the so-called Edwards-Anderson order parameter) [9]. 9. The behavior of correlation function, structural g(r) and non-ergodicity factor of the glass [6,9,12].10. The probability distribution of the for...

show abstract

Section: Discussionmentioning

confidence: 99%

Quantitative approximation schemes for glasses

Mangeat

Zamponi

2016

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…It should be noted that although the long-range positional order is obviously prevented in the two systems, the splitting second peaks in both g(r) and S(q) become more apparent as T decreases (note that this phenomenon is more evident for S(q)), which suggests the development of the locally preferred order with decreasing T and provides evidence that the model here has only weak frustration. The negligible effect of attractions on the static pair correlations indicates that the large difference seen in the relaxation dynamics cannot be explained at the static pair level [31]. In fact, it has been shown that considering locally preferred structures and higher-order static correlations can help to rationalize the effect of attractions on the relaxation dynamics [32,33].…”

Section: A Relaxation Dynamics and Static Pair Structurementioning

confidence: 99%

Effect of attractions on correlation length scales in a glass-forming liquid

Sun

2012

Phys. Rev. E

View full text Add to dashboard Cite

There is growing evidence that slow dynamics and dynamic heterogeneity possess structural signatures in glass-forming liquids. However, even in the weakly frustrated glass-forming liquids, whether or not the dynamic heterogeneity has a structural origin is a matter of debate. Via molecular dynamics simulation, we present a study of examining the connection between dynamic heterogeneity and bond orientational order in a weakly frustrated glass-forming liquid in two dimensions by taking advantage of assessing the effect of attractions on the correlation length scales. We find that attractions can strongly affect relaxation dynamics, dynamic heterogeneity and the associated dynamic correlation length of the liquid, but their influence on bond orientational order and the associated static correlation length shows a manner reminiscent of the effect of attractions on the thermodynamics of liquids. This implies that the growth of bond orientational order and static correlation length scale might be merely a manifestation of favoring the configurational entropy in weakly frustrated glass-forming liquids. Thus, our results lead strong evidence that bond orientational order cannot provide a complete description of dynamic heterogeneity even in weakly frustrated glass-forming systems.

show abstract

“…If such a treatment carries over to the analysis of dynamics, the expectation would be that liquids with LJ and the corresponding WCA interactions should have similar dynamics. However, in a series of recent papers, Bertheir and Tarjus have shown that model liquids with LJ and WCA interactions, exhibiting fairly similar structure, exhibit dramatically different dynamics, characterized by a structural relaxation time, at low temperatures [4][5][6][7]. In order to analyze this "non-perturbative" effect of the attractive forces on the dynamics, Berthier and Tarjus studied a number of "microscopic" approaches to predict the dynamics, based on knowledge of the static pair correlations.…”

mentioning

confidence: 99%

Role of Structure and Entropy in Determining Differences in Dynamics for Glass Formers with Different Interaction Potentials

et al. 2014

View full text Add to dashboard Cite

We present a study of two model liquids with different interaction potentials, exhibiting similar structure but significantly different dynamics at low temperatures. By evaluating the configurational entropy, we show that the differences in the dynamics of these systems can be understood in terms of their thermodynamic differences. Analyzing their structure, we demonstrate that differences in pair correlation functions between the two systems, through their contribution to the entropy, dominate the differences in their dynamics, and indeed overestimate the differences. Including the contribution of higher order structural correlations to the entropy leads to smaller estimates for the relaxation times, as well as smaller differences between the two studied systems.Many approaches towards understanding the dynamical behavior of liquids attempt to predict dynamics in terms of static structural correlations [1,2], often focussing on two-body correlation functions. In turn, it has been argued that the short range, repulsive interactions have a dominant role in determining the pair correlation function, with the attractions making a perturbative contribution. Such an approach was shown to be effective in predicting the pair correlation function for dense liquids interacting via. the Lennard-Jones (LJ) potential, by Weeks, Chandler and Andersen, who treated the LJ potential as a sum of a repulsive part (referred to subsequently as the WCA potential) and the attractive part [3]. If such a treatment carries over to the analysis of dynamics, the expectation would be that liquids with LJ and the corresponding WCA interactions should have similar dynamics. However, in a series of recent papers, Bertheir and Tarjus have shown that model liquids with LJ and WCA interactions, exhibiting fairly similar structure, exhibit dramatically different dynamics, characterized by a structural relaxation time, at low temperatures [4][5][6][7]. In order to analyze this "non-perturbative" effect of the attractive forces on the dynamics, Berthier and Tarjus studied a number of "microscopic" approaches to predict the dynamics, based on knowledge of the static pair correlations. They conclude that the approaches they analyze are unsuccessful in capturing the differences in dynamics between the LJ and WCA systems. Dyre and co-workers [8][9][10] have argued that the origins of these observations are not specifically in the inclusion or neglect of attractive interactions [10], but factors such as the inclusion of interactions of all first shell neighbors [8], and the presence or absence of scaling between systems/state points compared [9]. In particular, Pedersen and Dyre [9] identify a purely repulsive inverse-power-law (IPL) potential that has dynamics that can be mapped to the LJ case studied by Bertheir and Tarjus. These observations notwithstanding, the inability to capture the differences between the LJ and WCA system highlighted by Berthier and Tarjus by predictive approaches to dynamics remains an open issue. In this regard, it has been s...

show abstract

Critical test of the mode-coupling theory of the glass transition

Cited by 84 publications

References 36 publications

Quantitative approximation schemes for glasses

Quantitative approximation schemes for glasses

Effect of attractions on correlation length scales in a glass-forming liquid

Role of Structure and Entropy in Determining Differences in Dynamics for Glass Formers with Different Interaction Potentials

Contact Info

Product

Resources

About