Field theory of fluctuations in glasses

Franz, Silvio; Parisi, G.; Ricci-Tersenghi, Federico; Rizzo, Tommaso

doi:10.1140/epje/i2011-11102-0

Cited by 116 publications

(208 citation statements)

References 54 publications

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“…the spin overlap in spin-glass models or the density-density fluctuations in supercooled liquids. The case n = 0 is relevant for the continuous transition [31][32][33], the case n = 1 for the dynamic discontinuous transition [27][28][29]34]. The first result that we will derive in this paper is that, both in the continuous and discontinuous case, the exponent parameter λ is given by the ratio between the coefficients w 1 and w 2 of the static replicated Gibbs free energy:…”

Section: G(δq) = 1mentioning

confidence: 97%

“…This is a consequence of the similarity between (27) and (15). The expansion is written in terms of averages with respect to a dynamics in the potential (29) with the given value of Γ 0 . At leading order we have:…”

Section: Large Time Dynamics As An Expansion Around the Fast Motion Smentioning

confidence: 99%

“…Indeed states are only defined in the glassy phase away from the dynamical transition, therefore in order to evaluate the various W's at the critical point one should proceed by extrapolation. Alternatively a more safer procedure is to perform a dynamical evaluation similar to what was done in [29] for the two point functions G. In this case one should sit a the critical point and study six replicas with different thermal histories and the same equilibrium condition evaluating the W's (and correspondingly ω 1 and ω 2 ) as a function of time. A parametric plot in power of the average overlap could then be used in order to extract the critical value of the parameter exponent.…”

Section: Replicated Gibbs Free Energy and The Physical Observablesmentioning

confidence: 99%

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Critical dynamics in glassy systems

Parisi

Rizzo

2013

Phys. Rev. E

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Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the socalled parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.

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Section: G(δq) = 1mentioning

confidence: 97%

Section: Large Time Dynamics As An Expansion Around the Fast Motion Smentioning

confidence: 99%

Section: Replicated Gibbs Free Energy and The Physical Observablesmentioning

confidence: 99%

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Critical dynamics in glassy systems

Parisi

Rizzo

2013

Phys. Rev. E

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“…Therefore, by using these equations together with Eq. (27) we can estimate the correlation volume of transverse and longitudinal fluctuations, respectively given by…”

Section: Time Reparametrization Invariance and Fluctuationsmentioning

confidence: 99%

“…5(a) we show the ratio between the variances of local transverse fluctuations and longitudinal fluctuations, (δπ 1, r T ) 2 + (δπ 2, r T ) 2 / (δσ r ) 2 ("variance anisotropy ratio") [see Eq. (27)], as a function of the initial time t 1 . Similarly, in Fig.…”

Section: Fig 1: (Color Onlinementioning

confidence: 99%

Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems

2013

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We test a hypothesis for the origin of dynamical heterogeneity in slowly relaxing systems, namely that it emerges from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. We do this by constructing coarse grained observables and decomposing the fluctuations of these observables into transverse components, which are associated with the postulated time-fluctuation soft modes, and a longitudinal component, which represents the rest of the fluctuations. Our test is performed on data obtained in simulations of four models of structural glasses. As the hypothesis predicts, we find that the time reparametrization fluctuations become increasingly dominant as temperature is lowered and timescales are increased. More specifically, the ratio between the strengths of the transverse fluctuations and the longitudinal fluctuations grows as a function of the dynamical susceptibility, χ4, which represents the strength of the dynamical heterogeneity; and the correlation volumes for the transverse fluctuations are approximately proportional to those for the dynamical heterogeneity, while the correlation volumes for the longitudinal fluctuations remain small and approximately constant.

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Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

Douglas

Freed

2016

Advances in Chemical Physics

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We explore the nature of glass-formation in variable spatial dimensionality (d) based on the generalized entropy theory, a synthesis of the Adam-Gibbs model with direct computation of the configurational entropy of polymer fluids using an established statistical mechanical model. We find that structural relaxation in the fluid state asymptotically becomes Arrhenius in the d → ∞ limit and that the fluid transforms upon sufficient cooling above a critical dimension near d = 8 into a dense amorphous state with a finite positive residual configurational entropy. Direct computations of the isothermal compressibility and thermal expansion coefficient, taken to be physical measures of packing frustration, demonstrate that these fluid properties strongly correlate with the fragility of glass-formation.PACS numbers: 64.70.QGrowing evidence indicates that molecular packing plays an essential role in both the physics of crystallization [1][2][3][4][5] and glass-formation [6][7][8][9][10][11][12][13][14][15][16][17], prompting a consideration of variable spatial dimensionality (d) as a conceptual probe of these solidification processes. In particular, the "decorrelation principle", recently proposed by Torquato and Stillinger [18,19], states that unconstrained correlations in hard hyperspheres diminish with increasing d and vanish in the d → ∞ limit. Likewise, recent simulations [7][8][9] have indicated that certain often cited aspects of glass-formation, such as the dynamic heterogeneity and the decoupling between structural relaxation and diffusion, become diminished at elevated d. While prior studies [11][12][13][14][15] have focused mainly on how critical packing fractions associated with glass-formation in hard hyperspheres vary with d, little is known concerning the d dependence of the characteristic temperatures and fragility of glass-formation in molecular fluids. No prior work has considered complex fluids, such as polymeric liquids, where many molecular parameters may be tuned to control the nature of glass-formation.In this Letter, we consider the glass-formation of a model polymer glass-forming (GF) liquid in d dimensions. Our approach is based on the generalized entropy theory (GET) [20], which is a combination of the lattice cluster theory (LCT) [21] and the Adam-Gibbs (AG) theory [22] linking the configurational entropy s c (i.e., the entropy devoid of the vibrational component) to the structural relaxation time τ α . The LCT employs a ddimensional hypercubic lattice model, whose use facilitates the development of an expansion about the meanfield limit of infinite d. The LCT thus naturally provides * Contribution of the National Institute of Standards and Technology -Work not subject to copyright in the United States. † wsxu@uchicago.edu ‡ jack.douglas@nist.gov § freed@uchicago.edu a framework for considering the d dependence of polymer thermodynamic properties, thereby making the GET suitable for exploring glass-formation in d dimensions.As a primary result, we find that structural relaxation in the fluid st...

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Field theory of fluctuations in glasses

Cited by 116 publications

References 54 publications

Critical dynamics in glassy systems

Critical dynamics in glassy systems

Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems

Entropy Theory of Polymer Glass‐formation in Variable Spatial Dimension

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