Thermal origin of quasilocalized excitations in glasses

Ji, Wencheng; Geus, Tom W. J. de; Popović, Marko; Agoritsas, Elisabeth; Wyart, Matthieu

doi:10.1103/physreve.102.062110

Cited by 27 publications

(57 citation statements)

References 57 publications

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“…Yet, despite previous efforts [1,[22][23][24][25][26], we currently lack insight into the origin of QLMs' statistical-mechanical properties. Moreover, recent progress in studying computer glass-formers revealed intriguing properties of QLMs [17,18,27], e.g. the dependence of the amplitude A g of the ω 4 universal law on the state of glassy disorder (cf.…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Mean-field model of interacting quasilocalized excitations in glasses

et al. 2021

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“…In addition to usual phonons and other extended modes, in a variety of model glassy system it has been found the presence of low energy quasilocalized excitations with density of states (DOS) behaving quartically at low frequencies D QLS (ω) ∼ A ω 4 [1][2][3][4][5][6][7][8][9][10][11]. While the prefactor is found to depend on the details of the models and preparation protocols [10,11], the ω 4 behavior seems to be very general, independent of composition, preparation procedure and the space dimension [8,9,12]. Remarkably, the same ω 4 behavior of the DOS can be also found in a granular amorphous solid with long-range electroscatic interactions [13].…”

Section: Introductionmentioning

confidence: 99%

Delocalization transition in low energy excitation modes of vector spin glasses

Franz,

Nicoletti,

Parisi

et al. 2021

Preprint

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We study the energy minima of the fully-connected m-components vector spin glass model at zero temperature in an external magnetic field for m ≥ 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 λ m−1 in the paramagnetic phase and as √ λ 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 ≤ 2048 and compute the spectral properties, that show very strong corrections to the asymptotic scaling approaching the critical point.

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“…The coefficient A 4 on the other hand depends on the system and the preparation protocol. It appears that deeper states in the landscape, corresponding to better optimized glasses, have less and less the low energy excitations, reflecting in smaller and smaller values of A 4 , and correspondingly, the excitations are more and more localized [12,13]. This spectrum of localized modes was first rationalized through phenomenological theories [14,15], while new predictions have recently enriched the picture [11][12][13][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…Remarkably, low energy excitations of glasses display a high degree of universality. In addition to usual phonons, in a varity of model glassy system one finds the presence of ungapped low energy, quasi-localized excitiations with density of states (DOS) behaving quartically at low frequences ρ QLS (ω) ∼ A 4 ω 4 [1][2][3][4][5][6][7][8][9][10][11][12][13]. The ω 4 behavior seems to be very general, independent of the system, preparation protocol and even of the space dimension.…”

Section: Introductionmentioning

confidence: 99%

“…It appears that deeper states in the landscape, corresponding to better optimized glasses, have less and less the low energy excitations, reflecting in smaller and smaller values of A 4 , and correspondingly, the excitations are more and more localized [12,13]. This spectrum of localized modes was first rationalized through phenomenological theories [14,15], while new predictions have recently enriched the picture [11][12][13][16][17][18][19]. In addition to typical ungapped minima, found by usual minimization protocols, it has been noticed in [20] that in some model glasses gapped mimima can be found through the use of smart minimization protocols that include particle swap [21,22].…”

Section: Introductionmentioning

confidence: 99%

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Low energy excitations of mean-field glasses

Franz,

Nicoletti,

Ricci-Tersenghi

2022

Preprint

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We study the linear excitations around typical energy minima of a mean-field disordered model with continuous degrees of freedom undergoing a Random First Order Transition (RFOT). Contrary to naive expectations, the spectra of linear excitations are ungapped and we find the presence of a pseudogap corresponding to localized excitations with arbitrary low excitation energy. Moving to deeper minima in the landscape, the excitations appear increasingly localized while their abundance decreases. Beside typical minima, there also exist rare ultra-stable minima, with an energy gap and no localised excitations.

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Thermal origin of quasilocalized excitations in glasses

Cited by 27 publications

References 57 publications

Mean-field model of interacting quasilocalized excitations in glasses

Mean-field model of interacting quasilocalized excitations in glasses

Delocalization transition in low energy excitation modes of vector spin glasses

Low energy excitations of mean-field glasses

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