Low-frequency vibrations of jammed packings in large spatial dimensions

Shimada, Munekatsu; Mizuno, Hideyuki; Berthier, Ludovic; Ikeda, Atsushi

doi:10.1103/physreve.101.052906

Cited by 44 publications

(60 citation statements)

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“…Several other non-mean-field models [22,23] and phenomenological theories [1,[24][25][26] were previously put forward to the same aim; most of them, however, require parameter fine-tuning [22][23][24]26] or some rather strong a priori assumptions [1]. In addition, several other mean-field models, introduced in order to explain the low-frequency spectra of structural glasses, predict D(ω) ∼ ω 2 , independently of spatial dimension [16,[39][40][41]. In light of these previous efforts, our results appear to support -and further highlight -GPS's suggestion [19,20] that stabilizing anharmonicities -absent from the aforementioned mean-field models -constitute a necessary physical ingredient for observing the universal ∼ ω 4 law in this class of mean-field models.…”

Section: Discussionmentioning

confidence: 99%

“…1a) emerge from self-organized glassy frustration [8], which is generic to structural glasses quenched from a melt [9]. Their associated frequencies ω have been shown [10][11][12] to follow a universal nonphononic (non-Debye) density of states D(ω)∼ω 4 as ω→0, independently of microscopic details [13,14], spatial dimension [15,16] and formation history [17,18]. Some examples for D(ω), obtained in computer glasses, are shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

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Mean-field model of interacting quasilocalized excitations in glasses

et al. 2021

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Structural glasses feature quasilocalized excitations whose frequencies \omegaω follow a universal density of states {D}(\omega)\!\sim\!\omega^4D(ω)∼ω4. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff \kappa_0κ0) in the absence of interactions, interact among themselves through random couplings (characterized by a strength JJ) and with the surrounding elastic medium (an interaction characterized by a constant force hh). We first show that the model gives rise to a gapless density of states {D}(\omega)\!=\!A_{g}\,\omega^4D(ω)=Agω4 for a broad range of model parameters, expressed in terms of the strength of the oscillators’ stabilizing anharmonicity, which plays a decisive role in the model. Then — using scaling theory and numerical simulations — we provide a complete understanding of the non-universal prefactor A_{g}(h,J,\kappa_0)Ag(h,J,κ0), of the oscillators’ interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that A_{g}(h,J,\kappa_0)Ag(h,J,κ0) is a non-monotonic function of JJ for a fixed hh, varying predominantly exponentially with -(\kappa_0 h^{2/3}\!/J^2)−(κ0h2/3/J2) in the weak interactions (small JJ) regime — reminiscent of recent observations in computer glasses — and predominantly decays as a power-law for larger JJ, in a regime where hh plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mean-field model of interacting quasilocalized excitations in glasses

et al. 2021

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“…independent of spatial dimension [68,86], glass history [69], or interaction details [66]. The vibrational modes that populate this asymptotic scaling regime were shown to be quasilocalized; they feature a disordered core of size ξ g , decorated by algebraically decaying fields ∼r 1− d [21,87].…”

Section: A Density Per Frequency Of Quasilocalized Modesmentioning

confidence: 95%

Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions

et al. 2021

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“…For small ε, the tail behavior ρ(λ) ∼ λ m−1 ε m crosses-over as λ grows but still λ 1 to a conventional square root behavior ρ(λ) ∼ λ − λ * . In order to see this, we can rewrite Eq (12) as…”

Section: A Analytic Derivation Of the Lower Band Edge Spectrum In The Paramagnetic Phasementioning

confidence: 99%

Delocalization transition in low energy excitation modes of vector spin glasses

et al. 2022

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We study the energy minima of the fully-connected mm-components vector spin glass model at zero temperature in an external magnetic field for m\ge 3m≥3. The model has a zero temperature transition from a paramagnetic phase at high field to a spin glass phase at low field. We study the eigenvalues and eigenvectors of the Hessian in the minima of the Hamiltonian. The spectrum is gapless both in the paramagnetic and in the spin glass phase, with a pseudo-gap behaving as \lambda^{m-1}λm−1 in the paramagnetic phase and as \sqrt{\lambda}λ at criticality and in the spin glass phase. Despite the long-range nature of the model, the eigenstates close to the edge of the spectrum display quasi-localization properties. We show that the paramagnetic to spin glass transition corresponds to delocalization of the edge eigenvectors. We solve the model by the cavity method in the thermodynamic limit. We also perform numerical minimization of the Hamiltonian for N\le 2048N≤2048 and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

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Low-frequency vibrations of jammed packings in large spatial dimensions

Cited by 44 publications

References 50 publications

Mean-field model of interacting quasilocalized excitations in glasses

Mean-field model of interacting quasilocalized excitations in glasses

Mechanical disorder of sticky-sphere glasses. I. Effect of attractive interactions

Delocalization transition in low energy excitation modes of vector spin glasses

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