Publications (137)487.46 Total impact

Article: Comment on "Phase transition for quenched coupled replicas in a plaquette spin model of glasses'"
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ABSTRACT: This is a comment on the recent letter by Jack and Garrahan on "Phase transition for quenched coupled replicas in a plaquette spin model of glasses".  [Show abstract] [Hide abstract]
ABSTRACT: Motivated by the connection between the dynamical transition predicted by the meanfield theory of glassforming liquids and the spinodal of an Ising model in a quenched random field (RFIM) beyond meanfield, we revisit the phenomenon of spinodals in the presence of quenched disorder and develop a complete theory for it. By working at zero temperature in the quasistatically driven RFIM, thermal fluctuations are eliminated and one can give a rigorous content to the notion of spinodal. We show that the spinodal transition is due to the depinning and the subsequent expansion of rare droplets. We work out the critical behavior, which, in any finite dimension, is very different from the meanfield one: the characteristic length diverges exponentially and the thermodynamic quantities display very mild nonanalyticities much like in a Griffith phenomenon. On the basis of our results we assess the physical content and the status of the dynamical transition predicted by the meanfield theory of glassy dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: Slow dynamics in glassy systems is often interpreted as due to thermally activated events between "metastable" states. This emphasizes the role of nonperturbative fluctuations, which is especially dramatic when these fluctuations destroy a putative phase transition predicted at the meanfield level. To gain insight into such hard problems, we consider the implementation of a generic backandforth process, between microscopic theory and observable behavior via effective theories, in a toy model that is simple enough to allow for a thorough investigation: the onedimensional $\varphi^4$ theory at low temperature. We consider two ways of restricting the extent of the fluctuations, which both lead to a nonconvex effective potential (or free energy) : either through a finitesize system or by means of a running infrared cutoff within the nonperturbative Renormalization Group formalism. We discuss the physical insight one can get and the ways to treat strongly nonperturbative fluctuations in this context.  [Show abstract] [Hide abstract]
ABSTRACT: This work provide a thorough study of L\'evy or heavytailed random matrices (LM). By analysing the selfconsistent equation on the probability distribution of the diagonal elements of the resolvent we establish the equation determining the localisation transition and obtain the phase diagram of LMs. Using arguments based on supersymmetric field theory and Dyson Brownian motion we show that the eigenvalue statistics is the same one of the Gaussian Orthogonal Ensemble in the whole delocalised phase and is Poisson in the localised phase. Our numerics confirms these findings, valid in the limit of infinitely large LMs, but also reveals that the characteristic scale governing finite size effects diverges much faster than a power law approaching the transition and is already very large far from it. This leads to a very wide crossover region in which the system looks as if it were in a mixed phase. Our results, together with the ones obtained previously, provide now a complete theory of L\'evy matrices.  [Show abstract] [Hide abstract]
ABSTRACT: We develop a theory of amorphous interfaces in glassforming liquids. We show that the statistical properties of these surfaces, which separate regions characterized by different amorphous arrangements of particles, coincide with the ones of domain walls in the random field Ising model. A major consequence of our results is that supercooled liquids are characterized by two different static lengths: the pointtoset $\xi_{PS}$ which is a measure of the spatial extent of cooperative rearranging regions and the wandering length $\xi_\perp$ which is related to the fluctuations of their shape. We find that $\xi_\perp$ grows when approaching the glass transition but slower than $\xi_{PS}$. The wandering length increases as $s_c^{1/2}$, where $s_c$ is the configurational entropy. Our results strengthen the relationship with the random field Ising model found in recent works. They are in agreement with previous numerical studies of amorphous interfaces and provide a theoretical framework for explaining numerical and experimental findings on pinned particle systems and static lengths in glassforming liquids.  [Show abstract] [Hide abstract]
ABSTRACT: Recent works on hard spheres in the limit of infinite dimensions revealed that glass states, envisioned as metabasins in configuration space, can break up in a multitude of separate basins at low enough temperature or high enough pressure, leading to the emergence of new kinds of softmodes and unusual properties. In this paper we study by perturbative renormalisation group techniques the fate of this transition, which has been discovered in disordered meanfield models in the '80s. We find that the upper critical dimension d_u above which meanfield results hold is strictly larger than six and apparently nonuniversal, i.e. system dependent. Below d_u, we do not find any perturbative attractive fixed point (except for a tiny region of the 1RSB breaking parameter), thus showing that the transition in three dimensions either does not exist or changes nature from its meanfield counterpart. We also discuss some issues related to the low temperature full replica symmetry breaking phase found in infinite dimensions, as well as a possible relationship with the behavior of spin glasses in a field.  [Show abstract] [Hide abstract]
ABSTRACT: By using real space renormalisation group (RG) methods we show that spinglasses in a field display a new kind of transition in high dimensions. The corresponding critical properties and the spinglass phase are governed by two nonperturbative zero temperature fixed points of the RG flow. We compute the critical exponents, discuss the RG flow and its relevance for three dimensional systems. The new spinglass phase we discovered has unusual properties, which are intermediate between the ones conjectured by droplet and full replica symmetry breaking theories. These results provide a new perspective on the longstanding debate about the behaviour of spinglasses in a field. 
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ABSTRACT: We introduce a new disordered system, the SuperPotts model, which is a more frustrated version of the Potts glass. Its elementary degrees of freedom are variables that can take M values and are coupled via pairwise interactions. Its exact solution on a completely connected lattice demonstrates that for large enough M it belongs to the class of meanfield systems solved by a one step replica symmetry breaking Ansatz. Numerical simulations by the parallel tempering technique show that in three dimensions it displays a phenomenological behaviour similar to the one of glassforming liquids. The SuperPotts glass is therefore the first longsought disordered model allowing one to perform extensive and detailed studies of the Random First Order Transition in finite dimensions. We also discuss its behaviour for small values of M, which is similar to the one of spinglasses in a field.  [Show abstract] [Hide abstract]
ABSTRACT: We analyse, using Inhomogenous ModeCoupling Theory, the critical scaling behaviour of the dynamical susceptibility at a distance epsilon from continuous secondorder 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. 
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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 pointtoset 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.  [Show abstract] [Hide abstract]
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 longdistance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the randomfield Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration. We discuss to what extent this fieldtheoretical description and the mapping to the random field Ising model hold in the whole supercooled liquid regime, in particular near the glass transition.  [Show abstract] [Hide abstract]
ABSTRACT: In this work, we numerically investigate a new method for the characterization of growing length scales associated with spatially heterogeneous dynamics of glassforming liquids. This approach, motivated by the formulation of the inhomogeneous modecoupling 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 twopoint 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 fourpoint 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 meanfield approach to reach quantitative agreement. Advantages of our approach over the more conventional one based on fourpoint correlation functions are discussed.  [Show abstract] [Hide abstract]
ABSTRACT: We study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic lengthscale above which confinement effects become negligible is related to the pointtoset lengthscale introduced to measure the spatial extent of amorphous order in supercooled 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 pointtoset length). Finally, we discuss possible numerical and experimental tests of our predictions. 
Article: Perspective: The Glass Transition
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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. 
Article: Random pinning glass transition: Hallmarks, meanfield theory and renormalization group analysis
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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 meanfield analysis based on the study of pspin spherical disordered models and then obtain the threedimensional critical behavior by the MigdalKadanoff 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.  [Show abstract] [Hide abstract]
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 specificallydedicated experiments.  [Show abstract] [Hide abstract]
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 \(\vert {\chi }_{3}^{(3)}(\omega,T)\vert\) and \(\vert {\chi }_{3}^{(1)}(\omega,T)\vert\) 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 powerlaw 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. 
Article: Difference between level statistics, ergodicity and localization transitions on the Bethe lattice
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ABSTRACT: We show that noninteracting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but nonergodic, 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 freezingglass 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.
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5k  Citations  
487.46  Total Impact Points  
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Institutions

20142015

Université ParisSaclay
Lutetia Parisorum, ÎledeFrance, France


19992014

French National Centre for Scientific Research
 • Laboratoire Charles Coulomb
 • Laboratoire Statistique et Génome
Lutetia Parisorum, ÎledeFrance, France


20042013

Cea Leti
Grenoble, RhôneAlpes, France 
Institute of Geophysics, China Earthquake Administration
Peping, Beijing, China


2012

Atomic Energy and Alternative Energies Commission
 Institut de Physique Théorique (IPhT)
GifsurYvette, IledeFrance, France


2002

Université ParisSud 11
 Laboratoire de Physique Théorique et Modèles Statistiques
Orsay, ÎledeFrance, France


20012002

Rutgers, The State University of New Jersey
 Department Physics and Astronomy
New Brunswick, New Jersey, United States


19992001

Ecole Normale Supérieure de Paris
 Laboratoire de Physique Théorique
Paris, IledeFrance, France
