Universal Density of Low-Frequency States in Amorphous Solids at Finite Temperatures

Das, Prasenjit; Procaccia, Itamar

doi:10.1103/physrevlett.126.085502

Cited by 20 publications

(18 citation statements)

References 25 publications

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“…As such, the KHGPS Hamiltonian in Eq. (1) appears to offer a relatively simple model for the emergence of the universal D(ω) ∼ ω 4 nonphononic spectra, previously observed in finite-dimensional, particle-based computer glass-formers [10][11][12][13][14][15]18].…”

Section: Discussionmentioning

confidence: 78%

“…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: 78%

Section: Introductionmentioning

confidence: 99%

Mean-field model of interacting quasilocalized excitations in glasses

et al. 2021

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“…The main difference with respect to colloidal glasses is that, for molecular glasses, the spin glass susceptibility mildly changes upon decreasing temperature, something that has been interpreted as a signature of the absence of the Gardner transition. This goes along with the fact that soft spheres models display a density of states (DOS) that has a higher pseudogap, D(ω) ∼ ω 4 , [20][21][22][23][24][25][26][27] with respect to what is predicted by mean field theory in a typical Gardner phase where D(ω) ∼ ω 2 [28]. As a consequence, the spin glass susceptibility extracted from the harmonic density of states is finite.…”

Section: Introduction -mentioning

confidence: 94%

Marginal stability of soft anharmonic mean field spin glasses

Folena,

Urbani

2021

Preprint

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We investigate the properties of local minima of a recently introduced spin glass model of soft spins subjected to an anharmonic quartic local potential which serves as a model of low temperature molecular or soft glasses. We track the long time gradient descent dynamics in the glassy phase through dynamical mean field theory and show that spins are separated in two groups depending on their local stiffness. For spins having local stiffness that is right above its smallest possible value, the local fields distribution displays a depletion around the origin while those having a stiffness right below its largest possible value have a regular local fields distribution. We rationalize these findings through the replica method and show that the finite temperature phase transition to the glass phase is of continuous (full) replica-symmetry-breaking (RSB) type at all temperatures, down to zero temperature. Furthermore, marginal stability of the zero temperature fullRSB solution implies a linear pseudogap in the density of cavity fields for the spins with a local effective stiffness that is below a certain threshold. This generates a hole around the origin in the corresponding local field distribution. Those spins are natural candidates to model two level systems (TLS). The behavior of the cavity fields distribution for spins having stiffness close to the threshold one determines the tail of the low frequency density of states which is gapless. Therefore the spins having a stiffness around the cutoff one are the natural candidates to model quasi localized modes (QLM) in glasses.

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“…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%

Report on scipost_202102_00013v1

2021

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Structural glasses feature quasilocalized excitations whose frequencies ω follow a universal density of states D(ω) ∼ ω 4 . Yet, the underlying physics behind this universality is not yet 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 κ 0 ) in the absence of interactions, interact among themselves through random couplings (characterized by strength J) and with the surrounding elastic medium (an interaction characterized by a constant force h). We first show that the model gives rise to a gapless density of states D(ω) = A g ω 4 for a broad range of model parameters, expressed in terms of the strength of 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, κ 0 ), 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, κ 0 ) is a non-monotonic function of J for a fixed h, varying predominantly exponentially with −(κ 0 h 2/3 /J 2 ) in the weak interactions (small J) regime -reminiscent of recent observations in computer glasses -and predominantly decays as a power-law for larger J, in a regime where h 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. 3 The weak interactions regime 6 4 The intermediate-strength interactions regime 8 5 Conclusion 10 References 12

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Universal Density of Low-Frequency States in Amorphous Solids at Finite Temperatures

Cited by 20 publications

References 25 publications

Mean-field model of interacting quasilocalized excitations in glasses

Mean-field model of interacting quasilocalized excitations in glasses

Marginal stability of soft anharmonic mean field spin glasses

Report on scipost_202102_00013v1

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