Linear low energy excitations in fully-connected models of glasses

Franz, Silvio; Nicoletti, Flavio; Ricci-Tersenghi, Federico

doi:10.1088/1742-5468/ac6518

Cited by 5 publications

(11 citation statements)

References 65 publications

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“…It is possible to construct disordered mean-field models with localized low-energy modes or modes that are either localized or extended that correlate with local structure ( 39 – 42 ). However, existing numerical work on our system ( 7 ) suggests convergence to the spectrum of the perceptron, with zero density of low-frequency localized modes, as

at γ = 0, N finite.…”

Section: Resultsmentioning

confidence: 99%

“…It should be possible to capture such behavior in a mean-field description of structural glasses. For example, recent work has shown how mean-field spin glass models can have low-energy modes that localize on sites with a low local magnetic field (which acts as a heterogeneous structural variable) ( 41 , 42 ). In those models, this correlation is proven by studying the low-energy vibrational modes; as discussed above, however, our picture suggests that such a computation for structural glasses must be carried out at nonzero applied strain before the limit

is taken.…”

Section: Discussionmentioning

confidence: 99%

“… * We note that this is not a general property of mean-field theories, which may contain localized or even extended excitations that are correlated with notions of (simple) local structure ( 39 – 42 ), but of the current understanding of high- d structural glasses and the particular mean-field theory that has been developed for them. …”

mentioning

confidence: 99%

See 2 more Smart Citations

Correlation of plastic events with local structure in jammed packings across spatial dimensions

Ridout

Rocks

Liu

2022

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

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Significance Mean-field theories, exact in the limit of infinite spatial dimensions, succeed in describing many features of glasses and amorphous solids in low dimensions, leading to considerable effort to understand how behavior evolves with dimension. Until now, all evidence has supported a picture in which “localized physics,” responsible for deviations from mean-field behavior in low dimensions, fades away with rising dimension. Our work shows that rearrangements, in which particles change relative positions leading to fluid-like response, reveal a different picture of dimensional cross-over. We find that rearrangements, which are localized in two- and three-dimensional systems and correlated with local structure, remain just as correlated with local structure up to five dimensions, suggesting that local structure is important even in high dimensions.

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at γ = 0, N finite.…”

Section: Resultsmentioning

confidence: 99%

is taken.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Correlation of plastic events with local structure in jammed packings across spatial dimensions

Ridout

Rocks

Liu

2022

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

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“…For some specific distributions of h i , the condensation becomes a sharp phase transition in the limit of the large number of components [2]. Interestingly, this condensation transition has a similar mathematical structure of that of the Bose-Einstein condensation [2,[7][8][9].…”

Section: Introductionmentioning

confidence: 83%

Bose–Einstein-like condensation of deformed random matrix: a replica approach

Ikeda¹

2023

J. Stat. Mech.

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In this work, we investigate a symmetric deformed random matrix, which is obtained by perturbing the diagonal elements of the Wigner matrix. The eigenvector x m i n of the minimal eigenvalue λ m i n of the deformed random matrix tends to condensate at a single site. In certain types of perturbations and in the limit of the large components, this condensation becomes a sharp phase transition, the mechanism of which can be identified with the Bose–Einstein condensation in a mathematical level. We study this Bose–Einstein like condensation phenomenon by means of the replica method. We first derive a formula to calculate the minimal eigenvalue and the statistical properties of x m i n . Then, we apply the formula for two solvable cases: when the distribution of the perturbation has the double peak, and when it has a continuous distribution. For the double peak, we find that at the transition point, the participation ratio changes discontinuously from a finite value to zero. On the contrary, in the case of a continuous distribution, the participation ratio goes to zero either continuously or discontinuously, depending on the distribution.

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“…Moreover, we note that vectorial models for O(M) spins have been used recently in [27,28] to model the density of states in zero temperature amorphous solids. The model in equation ( 1) differs from [27,28] because of two points: (i) we consider real (unbounded) spins subjected to a random anharmonic (quartic) local potential which is essential for the physical behavior close to the mean field spin glass transition at zero temperature, and (ii) we include, as in [19], the adjacency matrix c and use the M → ∞ limit as a way to generate a field theory expansion at fixed and finite spatial dimension. For d → ∞ and M = 1 the model reduces to the KHGPS model as much as in the same limit the Edwards-Anderson model [29] gives the Sherrington-Kirkpatrick model [30].…”

Section: Definition Of the Modelmentioning

confidence: 99%

Field theory for zero temperature soft anharmonic spin glasses in a field

Urbani¹

2022

J. Phys. A: Math. Theor.

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We introduce a finite dimensional anharmonic soft spin glass in a field and show how it allows the construction a field theory at zero temperature and the corresponding loop expansion. The mean field level of the model coincides with a recently introduced fully connected model, the KHGPS model, and it has a spin glass transition in a field at zero temperature driven by the appearance of pseudogapped non-linear excitations. We analyze the zero temperature limit of the theory and the behavior of the bare masses and couplings on approaching the mean field zero temperature critical point. Focusing on the so called replicon sector of the field theory, we show that the bare mass corresponding to fluctuations in this sector is strictly positive at the transition in a certain region of control parameter space. At the same time the two relevant cubic coupling constants $g_1$ and $g_2$ show a non-analytic behavior in their bare values: approaching the critical point at zero temperature, $g_1\to \infty$ while $g_2\propto T$ with a prefactor diverging at the transition. Along the same lines we also develop the field theory to study the density of states of the model in finite dimension. We show that in the mean field limit the density of states converges to the one of the KHGPS model. However the construction allows a treatment of finite dimensional effects in perturbation theory.

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Linear low energy excitations in fully-connected models of glasses

Cited by 5 publications

References 65 publications

Correlation of plastic events with local structure in jammed packings across spatial dimensions

Correlation of plastic events with local structure in jammed packings across spatial dimensions

Bose–Einstein-like condensation of deformed random matrix: a replica approach

Field theory for zero temperature soft anharmonic spin glasses in a field

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