Giulio Biroli

Université Montpellier 2 Sciences et Techniques, Montpellier, Languedoc-Roussillon, France

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Publications (120)398.94 Total impact

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    ABSTRACT: We analyse, using Inhomogenous Mode-Coupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous second-order glass transitions. We find that the dynamical correlation length xi behaves generically as epsilon^{-1/3} and that the upper critical dimension is equal to six. More surprisingly, we find activated dynamic scaling, where xi grows with time as [ln(t)]^2 exactly at criticality. All these results suggest a deep analogy between the glassy behaviour of attractive colloids or randomly pinned supercooled liquids and that of the Random Field Ising Model.
    01/2014;
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    ABSTRACT: The dramatic dynamic slowing down associated with the glass transition is considered by many to be related to the existence of a static length scale that grows when temperature decreases. Defining, identifying, and measuring such a length is a subtle problem. Recently, two proposals, based on very different insights regarding the relevant physics, were put forward. One approach is based on the point-to-set correlation technique and the other on the scale where the lowest eigenvalue of the Hessian matrix becomes sensitive to disorder. Here we present numerical evidence that the two approaches might result in the same identical length scale. This provides mutual support for their relevance and, at the same time, raises interesting theoretical questions, discussed in the conclusion.
    Physical Review Letters 10/2013; 111(16):165701. · 7.94 Impact Factor
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    ABSTRACT: We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration. We discuss to what extent this field-theoretical description and the mapping to the random field Ising model hold in the whole supercooled liquid regime, in particular near the glass transition.
    09/2013;
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    ABSTRACT: In this work, we numerically investigate a new method for the characterization of growing length scales associated with spatially heterogeneous dynamics of glass-forming liquids. This approach, motivated by the formulation of the inhomogeneous mode-coupling theory (IMCT) [Biroli, G.; et al. Phys. Rev. Lett. 2006 97, 195701], utilizes inhomogeneous molecular dynamics simulations in which the system is perturbed by a spatially modulated external potential. We show that the response of the two-point correlation function to the external field allows one to probe dynamic correlations. We examine the critical properties shown by this function, in particular, the associated dynamic correlation length, that is found to be comparable to the one extracted from standardly employed four-point correlation functions. Our numerical results are in qualitative agreement with IMCT predictions but suggest that one has to take into account fluctuations not included in this mean-field approach to reach quantitative agreement. Advantages of our approach over the more conventional one based on four-point correlation functions are discussed.
    The Journal of Physical Chemistry B 07/2013; · 3.61 Impact Factor
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    ABSTRACT: We study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic length-scale above which confinement effects become negligible is related to the point-to-set length-scale introduced to measure the spatial extent of amorphous order in super-cooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions.
    Physical Review Letters 05/2013; 111(10). · 7.94 Impact Factor
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    ABSTRACT: We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, ϕ = ϕJ). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near ϕJ is divided in three different regimes separated by a characteristic temperature scale T(⋆)(ϕ) that vanishes quadratically with the distance to ϕJ. While two of them, (T < T(⋆)(ϕ), ϕ > ϕJ) and (T < T(⋆)(ϕ), ϕ < ϕJ), are described by harmonic theories developed in the zero temperature limit, the third one for T > T(⋆)(ϕ) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T(⋆)(ϕ) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.
    The Journal of Chemical Physics 03/2013; 138(12):12A507. · 3.16 Impact Factor
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    Giulio Biroli, Juan P Garrahan
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    ABSTRACT: We provide here a brief perspective on the glass transition field. It is an assessment, written from the point of view of theory, of where the field is and where it seems to be heading. We first give an overview of the main phenomenological characteristics, or "stylised facts," of the glass transition problem, i.e., the central observations that a theory of the physics of glass formation should aim to explain in a unified manner. We describe recent developments, with a particular focus on real space properties, including dynamical heterogeneity and facilitation, the search for underlying spatial or structural correlations, and the relation between the thermal glass transition and athermal jamming. We then discuss briefly how competing theories of the glass transition have adapted and evolved to account for such real space issues. We consider in detail two conceptual and methodological approaches put forward recently, that aim to access the fundamental critical phenomenon underlying the glass transition, be it thermodynamic or dynamic in origin, by means of biasing of ensembles, of configurations in the thermodynamic case, or of trajectories in the dynamic case. We end with a short outlook.
    The Journal of Chemical Physics 03/2013; 138(12):12A301. · 3.16 Impact Factor
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    Chiara Cammarota, Giulio Biroli
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    ABSTRACT: We present a detailed analysis of glass transitions induced by pinning particles at random from an equilibrium configuration. We first develop a mean-field analysis based on the study of p-spin spherical disordered models and then obtain the three-dimensional critical behavior by the Migdal-Kadanoff real space renormalization group method. We unveil the important physical differences with the case in which particles are pinned from a random (or very high temperature) configuration. We contrast the pinning particles approach to the ones based on biasing dynamical trajectories with respect to their activity and on coupling to equilibrium configurations. Finally, we discuss numerical and experimental tests.
    The Journal of Chemical Physics 03/2013; 138(12):12A547. · 3.16 Impact Factor
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    ABSTRACT: We give an overview of our recent works in which the a.c. nonlinear dielectric response of an archetypical glassformer (glycerol) was measured close to its glass transition temperature T g . The purpose was to investigate the prediction that the nonlinear susceptibility is directly related to the number of dynamically correlated molecules N { corr} (T). We explain that two nonlinear susceptibilities are available, namely χ3 (3) and χ3 (1), which correspond respectively to the nonlinear cubic response at the third harmonics and at the first harmonics. We describe how to measure these nonlinear responses, even if they yield signals much smaller than that of the linear response. We show that both \vert {χ }3^{(3)}(ω,T)\vert and \vert {χ }3^{(1)}(ω,T)\vert are peaked as a function of the angular frequency ω and mainly obeys critical scaling as a function of ωτα(T), where τα(T) is the relaxation time of the liquid. Both χ3 (3) and χ3 (1) decay with the same power-law of ω beyond the peak. The height of the peak increases as the temperature approaches T g : This yields an accurate determination of the temperature dependence of N { corr} (T), once the contribution of saturation of dipoles is disentangled from that of dynamical glassy correlations.
    01/2013;
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    ABSTRACT: We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase is a very heterogenous transport that proceeds over a few disorder dependent paths only. We show that the transition to the usual ergodic delocalized phase, which takes place for a disorder strength smaller than the one leading to the localization transition, is related to the freezing-glass transition of directed polymers in random media. The numerical study of level and eigenstate statistics, and of the singular properties of the probability distribution of the local density of states all support the existence of this new intermediate phase. Our results suggest that the localization transition may change nature in high dimensional systems.
    11/2012;
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    Bruno Sciolla, Giulio Biroli
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    ABSTRACT: Several mean-field computations have revealed the existence of an out of equilibrium dynamical transition induced by quantum quenching an isolated system starting from its symmetry broken phase. In this work we focus on the quantum phi^4 N-component field theory. By taking into account dynamical fluctuations at the Hartree-Fock level, corresponding to the leading order of the 1/N expansion, we derive the critical properties of the dynamical transition beyond mean-field theory (including at finite temperature). We find diverging time and length-scales, dynamic scaling and aging. Finally, we unveil a relationship with coarsening, an off-equilibrium dynamical regime that can be induced by quenching from the symmetric toward the symmetry broken phase.
    Physical Review B 11/2012; · 3.77 Impact Factor
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    ABSTRACT: We have measured, as a function of the age t_{a}, the aging of the nonlinear dielectric susceptibility χ_{3} of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time τ_{α}(t_{a}), this scaling breaks down for χ_{3}, suggesting an increase of the amplitude of χ_{3}. This is a strong indication that the number N_{corr} of molecules involved in relaxation events increases with t_{a}. For T=0.96×T_{g}, we find that N_{corr} increases by ∼10% when t_{a} varies from 1 to 100 ks. This sheds new light on the relation between length scales and time scales in glasses.
    Physical Review Letters 10/2012; 109(17):175702. · 7.94 Impact Factor
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    ABSTRACT: At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of "structural glasses", with a "random first-order transition" (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated e.g. with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension whereas, despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full-blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.
    Physical review. B, Condensed matter 10/2012; 87(6).
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    ABSTRACT: We present a comprehensive theoretical study of finite-size effects in the relaxation dynamics of glass-forming liquids. Our analysis is motivated by recent theoretical progress regarding the understanding of relevant correlation length scales in liquids approaching the glass transition. We obtain predictions both from general theoretical arguments and from a variety of specific perspectives: mode-coupling theory, kinetically constrained and defect models, and random first-order transition theory. In the last approach, we predict in particular a nonmonotonic evolution of finite-size effects across the mode-coupling crossover due to the competition between mode-coupling and activated relaxation. We study the role of competing relaxation mechanisms in giving rise to nonmonotonic finite-size effects by devising a kinetically constrained model where the proximity to the mode-coupling singularity can be continuously tuned by changing the lattice topology. We use our theoretical findings to interpret the results of extensive molecular dynamics studies of four model liquids with distinct structures and kinetic fragilities. While the less fragile model only displays modest finite-size effects, we find a more significant size dependence evolving with temperature for more fragile models, such as Lennard-Jones particles and soft spheres. Finally, for a binary mixture of harmonic spheres we observe the predicted nonmonotonic temperature evolution of finite-size effects near the fitted mode-coupling singularity, suggesting that the crossover from mode-coupling to activated dynamics is more pronounced for this model. Finally, we discuss the close connection between our results and the recent report of a nonmonotonic temperature evolution of a dynamic length scale near the mode-coupling crossover in harmonic spheres.
    Physical Review E 09/2012; 86(3-1):031502. · 2.31 Impact Factor
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    Chiara Cammarota, Giulio Biroli
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    ABSTRACT: We study the effect of freezing the positions of a fraction c of particles from an equilibrium configuration of a supercooled liquid at a temperature T. We show that within the random first-order transition theory pinning particles leads to an ideal glass transition for a critical fraction c = c(K)(T) even for moderate supercooling; e.g., close to the Mode-Coupling transition temperature. First we derive the phase diagram in the T - c plane by mean field approximations. Then, by applying a real-space renormalization group method, we obtain the critical properties for |c - c(K)(T)| → 0, in particular the divergence of length and time scales, which are dominated by two zero-temperature fixed points. We also show that for c = c(K)(T) the typical distance between frozen particles is related to the static point-to-set length scale of the unconstrained liquid. We discuss what are the main differences when particles are frozen in other geometries and not from an equilibrium configuration. Finally, we explain why the glass transition induced by freezing particles provides a new and very promising avenue of research to probe the glassy state and ascertain, or disprove, the validity of the theories of the glass transition.
    Proceedings of the National Academy of Sciences 06/2012; 109(23):8850-5. · 9.74 Impact Factor
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    Chiara Cammarota, Giulio Biroli
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    ABSTRACT: We obtain the patch-repetition entropy Sigma within the Random First Order Transition theory (RFOT) and for the square plaquette system, a model related to the dynamical facilitation theory of glassy dynamics. We find that in both cases the entropy of patches of linear size l, Sigma(l), scales as s_c l^d+A l^{d-1} down to length-scales of the order of one, where A is a positive constant, s_c is the configurational entropy density and d the spatial dimension. In consequence, the only meaningful length that can be defined from patch-repetition is the cross-over length xi=A/s_c. We relate xi to the typical length-scales already discussed in the literature and show that it is always of the order of the largest static length. Our results provide new insights, which are particularly relevant for RFOT theory, on the possible real space structure of super-cooled liquids. They suggest that this structure differs from a mosaic of different patches having roughly the same size.
    EPL (Europhysics Letters) 01/2012; 98(3). · 2.26 Impact Factor
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    Chiara Cammarota, Giulio Biroli
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    ABSTRACT: Pinning particles at random in supercooled liquids is a promising route to make substantial progress on the glass transition problem. Here we develop a mean-field theory by studying the equilibrium and non-equilibrium dynamics of the spherical p-spin model in presence of a fraction c of pinned spins. Our study shows the existence of two dynamic critical lines: one corresponding to usual Mode Coupling transitions and the other one to dynamic spinodal transitions. Quenches in the portion of the c - T phase diagram delimited by those two lines leads to aging. By extending our results to finite dimensional systems we predict non-interrupted aging only for quenches on the ideal glass transition line and two very different types of equilibrium relaxations for quenches below and above it.
    EPL (Europhysics Letters) 12/2011; 98(1). · 2.26 Impact Factor
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    Bruno Sciolla, Giulio Biroli
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    ABSTRACT: We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system. We apply our method to the Bose-Hubbard model, to a generalized Jaynes-Cummings model, and to the Ising model in a transverse field. We find that the quantum evolution can be mapped onto a classical effective dynamics, which involves only a few intensive observables. For some special parameters of the quench, peculiar dynamical transitions occur. They result from singularities of the classical effective dynamics and are reminiscent of the transition recently found in the fermionic Hubbard model. Finally, we discuss the generality of our results and possible extensions.
    Journal of Statistical Mechanics Theory and Experiment 08/2011; 11(11). · 1.87 Impact Factor
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    Giulio Biroli, Francesco Zamponi
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    ABSTRACT: We develop a quantum replica method for interacting particle systems and use it to estimate the location of the glass transition line in Helium 4. Although we do not fully succeed in taking into account all quantum effects, we make a thorough semiclassical analysis. We confirm previous suggestions that quantum fluctuations promote the formation of the glass and give a quantitative estimate of this effect at high density. Finally, we discuss the difficulties that are met when one tries to extend the calculation to the region of low densities and low temperatures, where quantum effects are strong and the semiclassical expansion breaks down.
    Journal of Low Temperature Physics 07/2011; · 1.18 Impact Factor
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    ABSTRACT: We have measured the ac nonlinear dielectric response χ3 (ω, T) of an archetypical glassformer (glycerol) just above its glass transition temperature Tg ∼190 K. Our measurements were performed at temperatures between Tg + 4 K and Tg + 35 K, which corresponds to 5 decades of variation of the relaxation time τ (T) of the liquid. We find that χ3(ω, T) is peaked for ωτ ∼ 0.2 and that the height of the peak grows as one approaches Tg. A powerlaw in frequency beyond the peak of χ3 is observed and χ3 (ω, T) displays scaling as a function of ωτ.These features correspond to the main predictions of some recent theoretical works relating the nonlinear susceptibility of supercooled liquids to the average number Ncorr of dynamically correlated molecules. We thus interpret the experimental increase of the peak of nonlinear susceptibility when T decreases, as an increase of Ncorr when T → Tg. This strongly reinforces the collective picture of the dynamics of supercooled liquids close to the glass transition. Finally, we discuss some heating effects and show that they do not affect significantly our conclusions. (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
    physica status solidi (c) 03/2011; 8(11‐12):3147 - 3150.

Publication Stats

2k Citations
398.94 Total Impact Points

Institutions

  • 2013
    • Université Montpellier 2 Sciences et Techniques
      • Laboratoire Charles Coulomb (L2C)
      Montpellier, Languedoc-Roussillon, France
  • 2005–2012
    • Cea Leti
      Grenoble, Rhône-Alpes, France
  • 2004–2012
    • Atomic Energy and Alternative Energies Commission
      • Institut de Physique Théorique (IPhT)
      Gif-sur-Yvette, Ile-de-France, France
    • Sapienza University of Rome
      • Department of Physics
      Roma, Latium, Italy
  • 2010
    • Columbia University
      • Department of Chemistry
      New York City, NY, United States
  • 1999–2010
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2009
    • Pierre and Marie Curie University - Paris 6
      • Laboratoire de Physique Théorique et des Hautes Energies (LPTHE)
      Paris, Ile-de-France, France
  • 2001–2006
    • Ecole Normale Supérieure de Paris
      • Laboratoire de Physique Théorique
      Paris, Ile-de-France, France
  • 2002
    • Université Paris-Sud 11
      • Laboratoire de Physique Théorique et Modèles Statistiques
      Orsay, Île-de-France, France
  • 2001–2002
    • Rutgers, The State University of New Jersey
      • Department Physics and Astronomy
      New Brunswick, NJ, United States