Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco

doi:10.1146/annurev-conmatphys-031016-025334

Cited by 305 publications

(455 citation statements)

References 132 publications

(219 reference statements)

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“…Future work should clarify these connections, both by additional numerical simulations and analytical calculations. The emergence of slow dynamics at low temperature, accompanied by the non-trivial change in the vibrations of the particles, is reminiscent of the mean field scenario where these features are consequences of an underlying phase transition, called the Gardner transition [47,48], which separates a high-temperature normal solid and a low-temperature marginally stable solid. While our results, similarly to the ones of Ref.…”

Section: Discussionmentioning

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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Section: Discussionmentioning

confidence: 99%

Low-temperature anomalies of a vapor deposited glass

Seoane

Reid

Pablo

et al. 2018

Phys. Rev. Materials

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“…Moreover, the average contact force is proportional to the pressure, [1], which indeed vanishes at jamming. For contacts, one can thus define scaled forces f s µ = [1] f µ /p, that remain finite at the jamming transition. These scaled forces still satisfy the condition T f s = 0, where the matrix is calculated at the jamming point.…”

Section: Some Consequences Of Isostaticity: Force Distribution and Somentioning

confidence: 95%

“…The exact description of the glassy phases of high-dimensional sphere systems and the discovery that universal predictions at jamming match finite dimensional observations [1] has renewed the interest in the statistical physics of random constraint satisfaction problems (CSP) with continuous variables. In CSPs, one seeks assignments of a set of N variables that satisfy a system of constraints.…”

Section: Introductionmentioning

confidence: 99%

“…This SAT/UNSAT threshold is clearly analogue to the jamming transition in soft-spheres [5,6], that separates the low density region where spheres do not overlap from the high density one where no-overlap configurations do not exist. The jamming transition in spheres has highly universal features, with exponents that appear to be independent of the dimension and of the protocol used to produce the jammed configurations [1,[5][6][7][8][9][10][11][12]. While some exponents, like e.g.…”

Section: Introductionmentioning

confidence: 99%

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Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

et al. 2017

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Random constraint satisfaction problems (CSP) have been studied extensively using statistical physics techniques. They provide a benchmark to study average case scenarios instead of the worst case one. The interplay between statistical physics of disordered systems and computer science has brought new light into the realm of computational complexity theory, by introducing the notion of clustering of solutions, related to replica symmetry breaking. However, the class of problems in which clustering has been studied often involve discrete degrees of freedom: standard random CSPs are random K-SAT (aka disordered Ising models) or random coloring problems (aka disordered Potts models). In this work we consider instead problems that involve continuous degrees of freedom. The simplest prototype of these problems is the perceptron. Here we discuss in detail the full phase diagram of the model. In the regions of parameter space where the problem is non-convex, leading to multiple disconnected clusters of solutions, the solution is critical at the SAT/UNSAT threshold and lies in the same universality class of the jamming transition of soft spheres. We show how the critical behavior at the satisfiability threshold emerges, and we compute the critical exponents associated to the approach to the transition from both the SAT and UNSAT phase. We conjecture that there is a large universality class of non-convex continuous CSPs whose SAT-UNSAT threshold is described by the same scaling solution.

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“…In a seminal paper 1 , an universal jamming phase diagram was proposed to unify the transition of structural arrest of different systems, including the glass and the jamming transitions. However, within a mean field or the infinite dimensionality limit a distinction between the glass transition of liquids and the jamming transition of granular materials was posed in an analytical study of frictionless hard sphere particles [3][4][5][6][7] . As illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

2017

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We investigate the glass and the jamming transitions of hard spheres in finite dimensions d, through a revised cell theory, that combines the free volume and the Random First Order Theory (RFOT). Recent results show that in infinite dimension the ideal glass transition and jamming transitions are distinct, while based on our theory we argue that they indeed coincide for finite d. As a consequence, jamming results into a percolation transition described by RFOT, with a static length diverging with exponent ν = 2/d, which we verify through finite size scaling, and standard critical exponents α = 0, β = 0 and γ = 2 independent on d.

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Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions

Cited by 305 publications

References 132 publications

Low-temperature anomalies of a vapor deposited glass

Low-temperature anomalies of a vapor deposited glass

Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems

Universal behaviour of the glass and the jamming transitions in finite dimensions for hard spheres

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