Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed 
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-Spin Model

The concept of jamming has attracted great research interest due to its broad relevance in soft-matter, such as liquids, glasses, colloids, foams, and granular materials, and its deep connection to sphere packing and optimization problems. Here, we show that the domain of amorphous jammed states of frictionless spheres can be significantly extended, from the well-known jamming-point at a fixed density, to a jamming-plane that spans the density and shear strain axes. We explore the jamming-plane, via athermal and thermal simulations of compression and shear jamming, with initial equilibrium configurations prepared by an efficient swap algorithm. The jamming-plane can be divided into reversible-jamming and irreversible-jamming regimes, based on the reversibility of the route from the initial configuration to jamming. Our results suggest that the irreversible-jamming behavior reflects an escape from the metastable glass basin to which the initial configuration belongs to or the absence of such basins. All jammed states, either compression- or shear-jammed, are isostatic and exhibit jamming criticality of the same universality class. However, the anisotropy of contact networks nontrivially depends on the jamming density and strain. Among all state points on the jamming-plane, the jamming-point is a unique one with the minimum jamming density and the maximum randomness. For crystalline packings, the jamming-plane shrinks into a single shear jamming-line that is independent of initial configurations. Our study paves the way for solving the long-standing random close-packing problem and provides a more complete framework to understand jamming.

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“…Therefore, the generalization of the calculation in ref. 50 to sphere systems would be very appealing.…”

Section: Discussionmentioning

confidence: 99%

A jamming plane of sphere packings

Jin

Yoshino

2021

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

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“…We set a = 0.3, as it is a common choice used in literature[36] 4. A similar phenomenology that has enabled the identification of the onset temperature via the overlap has recently been observed in diverse systems, ranging from the mixed p-spin model[37] to the 3D Heisenberg spin glass[38].…”

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confidence: 99%

Revisiting the concept of activation in supercooled liquids

Baity‐Jesi

Biroli²,

Reichman

2021

Eur. Phys. J. E

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In this work, we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature $$T_{\mathrm{o}}$$ T o and mode-coupling temperature $$T_{\mathrm{c}}$$ T c . First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed $$\tau _{\alpha }$$ τ α by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.

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“…Marginal states of different energy can also be reached asymptotically by the dynamics, as shown for instance in Ref. [9], provided that the system is initialized at lower temperatures.…”

Section: Introductionmentioning

confidence: 80%

“…Similarly, the integration on the elements m a N −1 N −1 in U 1 is free, while the elements m a N −1 N and m a N N are constrained to take a given value. To decouple the constrained matrix elements from the unconstrained ones, we make use of Gaussian conditioning 9 . Introducing the vector notation Ξ αβ = (Ξ 1 αβ , Ξ 2 αβ ) T and imposing m a αN = 0, we obtain:…”

Section: B Derivation Of Eq 23mentioning

confidence: 99%

Dynamical instantons and activated processes in mean-field glass models

Biroli

Cammarota

2021

SciPost Phys.

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We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical p-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

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Rethinking Mean-Field Glassy Dynamics and Its Relation with the Energy Landscape: The Surprising Case of the Spherical Mixed p -Spin Model

Cited by 49 publications

References 52 publications

A jamming plane of sphere packings

A jamming plane of sphere packings

Revisiting the concept of activation in supercooled liquids

Dynamical instantons and activated processes in mean-field glass models

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