Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model

Jaubert, Ludovic D. C.; Chamon, Claudio; Cugliandolo, Leticia F.; Picco, Marco

doi:10.1088/1742-5468/2007/05/p05001

Cited by 26 publications

(76 citation statements)

References 98 publications

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“…The characteristic times of the exponential and stretched exponential are e ϭ 9,950 s ( ϭ 0.52), 23,000 s ( ϭ 0.56), and s ϭ 10,650 s ( ϭ 0.52), and 43,400 s ( ϭ 0.56), respectively, and the stretching exponent is ␤ ϭ 0.85 ( ϭ 0.52) and ␤ ϭ 0.65 ( ϭ 0.56). Still, it is interesting to note that this behavior is remarkably similar to the one found with Monte Carlo simulations of the 3d Edwards-Anderson (EA) spin glass (21).…”

Section: Discussionsupporting

confidence: 76%

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From particles to spins: Eulerian formulation of supercooled liquids and glasses

Chamon¹,

Cugliandolo²,

Fabricius³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

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The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also nontransparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids and glasses that allows for a simple connection between particle and spin systems, and that permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin glasses. We apply this framework to the study of the dynamics of colloidal particle suspensions for packing fractions corresponding to the supercooled and glassy regimes, which are probed via confocal microscopy.dynamics ͉ structural T he phenomenology of structural and spin glasses has much in common: no static long-range order, aging relaxation, heterogeneous dynamics, and so on (for reviews, see refs. 1 and 2). Although a precise and unambiguous connection between these two problems is still lacking, the possibility that such relation exists dates back to the work by Kirkpatrick, Thirumalai,, who proposed a connection between structural glasses and fully connected p-spin disordered models. These mean-field spin models have a dynamic phase transition that mimics the glassy arrest at T g and a static phase transition at a lower temperature T s that realizes the Kauzmann entropy crisis. The spin dynamics is sluggish above and close to T g as in supercooled liquids and the system falls out of equilibrium below T g and shows aging as in a glass (1, 9). More recently, Tarzia and Moore (10) have paralleled the phenomenology of structural glasses to that of an Edwards-Anderson model in a uniform magnetic field. One of the main hurdles in making a direct real space connection between structural and spin glasses is that disordered spin models are defined on a lattice, whereas the particles comprising structural glasses are itinerant.Supercooled liquids and glasses are usually described within the Lagrangian formulation, in which one tracks the position of individual particles as a function of time. Natural quantities computed within this frame of reference are the particle's mean-square displacement and self-diffusion. Heterogeneous dynamics can be probed, for example, by studying quantities such as mobility within prescribed boxes; however, such fixed regions serve this purpose just for a certain time, because particles move in and out of these boxes if one waits for long enough. In contrast, studying local dynamics in a spin glass presents no such complication, because spins remain fixed to their sites at all times, and all that changes is the spin orientation as a function of time. Therefore, if one is to construct a simple d...

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Section: Discussionsupporting

confidence: 76%

“…Such formulation does not rely on tracking individual particles over time, but instead it focuses on fixed locations at each time, without regard to the particle identity at the given site. This approach permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin models (21)(22)(23)31).…”

Section: Discussionmentioning

confidence: 99%

From particles to spins: Eulerian formulation of supercooled liquids and glasses

Chamon¹,

Cugliandolo²,

Fabricius³

et al. 2008

Proc. Natl. Acad. Sci. U.S.A.

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“…The origin of SHD is still uncertain, in part because of the lack of direct microscopic tests to attempt to disprove proposed theories [6,[9][10][11]. Here we apply one such test [12] for the hypothesis that SHD is associated with fluctuations in the time variable [11,13,14], and find that our molecular dynamics data are consistent with the hypothesis. This test can also be applied to particle tracking experimental data in colloidal [4] and granular systems [8], thus allowing to investigate a possible unified explanation of SHD in diverse systems.…”

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confidence: 79%

Mapping Dynamical Heterogeneity in Structural Glasses to Correlated Fluctuations of the Time Variables

2011

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Dynamical heterogeneities -strong fluctuations near the glass transition -are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data from four glass-forming models to construct coarse grained observables that probe the dynamical heterogeneity, and decompose the fluctuations of these observables into two transverse components associated with the postulated time-fluctuation soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and timescales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with the correlation volumes of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.

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“…(14). This result, however, is expected to apply only within the limits of the approximation, that is to say, when C is not too close to 1 nor to −1.…”

Section: Non Interacting Interfaces Approximationmentioning

confidence: 92%

“…In Sec. III, after defining the restricted average and the methods used to measure it, we check the validity of the Ansatz (13) and (14) in various systems. Specifically, in Sec.…”

Section: Introductionmentioning

confidence: 99%

Fluctuations and effective temperatures in coarsening

Corberi

Cugliandolo

2009

J. Stat. Mech.

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We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called χ and C, the averages of which yield the self linear response and correlation function. We introduce a restricted average of the χ's, summing over all configurations with a given value of C. We find that the restricted average χ C obeys a scaling form, and that the slope of the scaling function approaches the universal value X∞ of the limiting effective temperature in the long-time limit and for C → 0. Our results tend to confirm the expectation that time-reparametrization invariance is not realized in coarsening systems at criticality. Finally, we discuss possible experimental tests of our proposal.

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Growing dynamical length, scaling, and heterogeneities in the 3D Edwards–Anderson model

Cited by 26 publications

References 98 publications

From particles to spins: Eulerian formulation of supercooled liquids and glasses

From particles to spins: Eulerian formulation of supercooled liquids and glasses

Mapping Dynamical Heterogeneity in Structural Glasses to Correlated Fluctuations of the Time Variables

Fluctuations and effective temperatures in coarsening

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