Marginal Stability in Structural, Spin, and Electron Glasses

Müller, Markus; Wyart, Matthieu

doi:10.1146/annurev-conmatphys-031214-014614

Cited by 180 publications

(278 citation statements)

References 123 publications

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“…20 it was observed that contact-opening excitations in packings are marginally stable, so that the bounds 14 and 15 are satisfied with equality, with numerical values γ ≈ 0:4, θ ℓ ≈ 0:17, and θ e ≈ 0:44. Saturation of [15] was recently proven for certain dynamics (38). Assuming such marginal stability, it follows that θ f = θ ℓ < θ e and the exponent θ e can be determined from θ e = 2θ f =ð1 − θ f Þ ≈ 0:41, a value consistent with the direct measurement 0.44.…”

Section: Hard Spheressupporting

confidence: 66%

Force distribution affects vibrational properties in hard-sphere glasses

DeGiuli

Lerner

Brito

et al. 2014

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

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121

166

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We theoretically and numerically study the elastic properties of hard-sphere glasses and provide a real-space description of their mechanical stability. In contrast to repulsive particles at zero temperature, we argue that the presence of certain pairs of particles interacting with a small force f soften elastic properties. This softening affects the exponents characterizing elasticity at high pressure, leading to experimentally testable predictions. Denoting P(f ) ∼ f θe , the force distribution of such pairs and ϕ c the packing fraction at which pressure diverges, we predict that (i) the density of states has a low-frequency peak at a scale ω*, rising up to it as D(ω) ∼ ω 2+a , and decaying above ω* as D(ω) ∼ ω −a where a = (1 − θ e )=(3 + θ e ) and ω is the frequency, (ii) shear modulus and mean-squared displacement are inversely proportional with 〈δR 2 〉 ∼ 1=μ ∼ (ϕ c − ϕ) κ , where κ = 2 − 2=(3 + θ e ), and (iii) continuum elasticity breaks down on a scale ℓ c ∼ 1= ffiffiffiffiffi δz p ∼ (ϕ c − ϕ) −b , where b = (1 + θ e )=(6 + 2θ e ) and δz = z − 2d, where z is the coordination and d the spatial dimension. We numerically test (i) and provide data supporting that θ e ≈ 0:41 in our bidisperse system, independently of system preparation in two and three dimensions, leading to κ ≈ 1:41, a ≈ 0:17, and b ≈ 0:21. Our results for the mean-square displacement are consistent with a recent exact replica computation for d = ∞, whereas some observations differ, as rationalized by the present approach.colloids | glass transition | marginal stability | boson peak | jamming T he emergence of rigidity near the glass transition is a fundamental and highly debated topic in condensed matter and is perhaps most surprising in hard-sphere glasses where rigidity is purely entropic in nature. The rapid growth of relaxation time around a packing fraction ϕ g ≈ 0:58 suggests that metastable states have appeared in the free-energy landscape, and that activation above barriers is required for the system to flow (1). This scenario is presumably what mode-coupling theory captures (2, 3) and can be rationalized via density functional theory (4) and via the replica method (5). Recently a real-space description of mechanical stability and elasticity in hard-sphere glasses has been proposed (6, 7), which is most easily tested at large pressure, deep in the glass phase. It is based on two results. First, in elastic networks and athermal packings of soft spheres (8-10), mechanical stability is controlled by the mean number of contacts per particle, or coordination z (as already discussed by Maxwell in ref. 11), and the applied compressive strain e (10). As one may intuitively expect, increasing coordination is stabilizing, whereas increasing pressure at fixed coordination is destabilizing. Second, within a long-lived metastable state the vibrational free energy of a hard-sphere system can be approximated as a sum of local interaction terms between pairs of colliding particles, which are said to be in contact. On a time scale that contains many...

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Section: Hard Spheressupporting

confidence: 66%

Force distribution affects vibrational properties in hard-sphere glasses

DeGiuli

Lerner

Brito

et al. 2014

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

Self Cite

121

166

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“…Moreover, it is certainly worth exploring the implications of our results on the statistics of avalanches induced by strain, generalizing the ideas originally put forward in ref. 2, and connect our results with studies on shear-transformation-zone interactions 21 . All these factors open the way towards new research directions aimed at revealing the true nature of glasses.…”

supporting

confidence: 67%

“…In ref. 21, it was argued that this is due to the way in which they are formed: unstable elementary excitations progressively rarify during a crunch, and jamming takes place exactly when no excitation is left, leaving the system solid but at the verge of instability (that is, marginally stable). Within mean-field theory, the results found at jamming are a consequence of a more general marginal stability: the appearance of multiple competing particle arrangements is accompanied by the emergence of long-range power-law correlations and soft modes.…”

mentioning

confidence: 99%

Breakdown of elasticity in amorphous solids

2016

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What characterizes a solid is the way that it responds to external stresses. Ordered solids, such as crystals, exhibit an elastic regime followed by a plastic regime, both understood microscopically in terms of lattice distortion and dislocations. For amorphous solids the situation is instead less clear, and the microscopic understanding of the response to deformation and stress is a very active research topic. Several studies have revealed that even in the elastic regime the response is very jerky at low temperature, resembling very much the response of disordered magnetic materials 1-6 . Here we show that in a very large class of amorphous solids this behaviour emerges upon decreasing temperature, as a phase transition, where standard elastic behaviour breaks down. At the transition all nonlinear elastic moduli diverge and standard elasticity theory no longer holds. Below the transition, the response to deformation becomes history-and time-dependent.Our work connects two different lines of research on amorphous solids such as structural, colloidal and granular glasses. The first focuses on their behaviour at low temperature. With the aim of understanding the response of glasses to deformations, there have been extensive numerical studies of stress versus strain curves obtained by quenching model systems at zero temperature. One of the main outcomes is that the increase of the stress is punctuated by sudden drops related to avalanche-like rearrangements both before and after the yielding point [1][2][3][4][5][6] . This behaviour makes the measurements, and even the definition of elastic moduli fairly involved. In a series of works, Procaccia et al. have given evidence that in some models of glasses, such as Lennard-Jones mixtures (and variants), nonlinear elastic moduli exhibit diverging fluctuations, and linear elastic moduli differ depending on the way they are defined from the stress-strain curve 7,8 . Another independent research stream has focused on gaining an understanding of the jamming and glass transitions of hard spheres both from real-space and mean-field theory perspectives 9,10 . The exact solution obtained in the limit of infinite dimensions revealed that by increasing the pressure a hard sphere glass exhibits a transition within the solid phase, where multiple arrangements emerge as different competing solid phases 11,12 . This is called the Gardner transition, in analogy with previous results in disordered spin models 13,14 . Recent simulations have confirmed that in three dimensions these different arrangements indeed become increasingly long-lived, possibly leading to ergodicity breaking 15 . These mean-field analyses complement and strengthen all the remarkable results found in the past two decades on jammed hard spheres glasses. The major outcome of these real-space studies was the discovery that amorphous jammed solids are marginally stable-that is, characterized by soft modes and critical behaviour, and in consequence by properties which are very different from those of usual crystalline ...

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“…It has been suggested by previous work [28,31,32] that, below the threshold T * , the system might be "marginally stable", i.e. characterized by a diverging correlation length of particle displacements, and a diverging χ AB , also associated to delocalized soft vibrational modes [40,41]. However, Ref.…”

Section: Aging and Heterogeneity Of Individual Samplesmentioning

confidence: 99%

Low-temperature anomalies of a vapor deposited glass

Seoane

Reid

Pablo

et al. 2018

Phys. Rev. Materials

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We investigate the low temperature properties of two-dimensional Lennard-Jones glass films, prepared in silico both by liquid cooling and by physical vapor deposition. We identify deep in the solid phase a crossover temperature T * , at which slow dynamics and enhanced heterogeneity emerge. Around T * , localized defects become visible, leading to vibrational anomalies as compared to standard solids. We find that on average, T * decreases in samples with lower inherent structure energy, suggesting that such anomalies will be suppressed in ultra-stable glass films, prepared both by very slow liquid cooling and vapor deposition.Low-temperature crystalline solids are usually described in terms of harmonic vibrations around a perfect periodic lattice (phonons). Within this framework, defects such as vacancies and dislocations can be treated as small perturbations. This description breaks down for amorphous solids such as glasses, foams, emulsions, plastics, colloids, granular materials, bacterial colonies, and tissues [1][2][3][4][5][6][7]. In these systems, the identification of "defects" becomes challenging because the solid ground state is strongly disordered. As a consequence, amorphous solids display many universal anomalies with respect to crystals. Examples are the so-called Boson Peak, an excess of low-energy vibrational modes [8]; the anomalous scaling of heat capacity and thermal conductivity with temperature [9,10]; the irreversible plastic response to arbitrarily small perturbations [1,3,4,11]; and highly cooperative relaxation dynamics, contributing to the socalled β-processes [12][13][14].These anomalies have been widely reported in amorphous solids of very different nature. Interestingly, recent experimental work has shown that by preparing glasses through a process of physical vapor deposition, one can produce ultra-stable states that lie deep in the free energy landscape [15]. Compared to their liquid-cooled counterparts, vapor-deposited glasses show higher density [16] and kinetic stability [15,17]. When these ultra-stable glasses are studied at very low temperatures, it is found that the anomalies characteristic of amorphous solids are strongly supressed [18][19][20][21][22].Many theoretical approaches to this problem are based on the study of the potential energy landscape of glassforming particle systems [13,[23][24][25][26][27][28]. These studies have suggested that glass anomalies can be interpreted in terms of glass states being not well-defined energy minima, but structured metabasins containing a collection of sub-basins separated by barriers of variable size [29,30], see Fig. 1. In particular, recent work [31][32][33] has identified a set of simple observables (the mean square displacement between identical "clones" of the original system) that allows one to detect easily the development of a structure of sub-basins inside a glass metabasin.In this work, using the methods of [31-33], we explore in silico the potential energy landscape of binary Lennard-Jones glass films prepared through tw...

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Marginal Stability in Structural, Spin, and Electron Glasses

Cited by 180 publications

References 123 publications

Force distribution affects vibrational properties in hard-sphere glasses

Force distribution affects vibrational properties in hard-sphere glasses

Breakdown of elasticity in amorphous solids

Low-temperature anomalies of a vapor deposited glass

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