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Ludovic Berthier

Publications and source records attributed to Ludovic Berthier.

At least 217 records · Page 12Linked to original sources
arXiv2004

Dynamic criticality in glass-forming liquids

We propose that the dynamics of supercooled liquids and the formation of glasses can be understood from the existence of a zero temperature dynamical critical point. To support our proposal, we derive from simple physical assumptions a dynamic field theory for supercooled liquids, which we study using the renormalization group (RG). Its long time behaviour is dominated by a zero temperature critical point, which for dimensions d > 2 belongs to the directed percolation universality class. Molecular dynamics simulations confirm the existence of dynamic scaling behaviour consistent with the RG predictions.

cond-mat.soft↗
arXiv2003

Time and length scales in supercooled liquids

We numerically obtain the first quantitative demonstration that development of spatial correlations of mobility as temperature is lowered is responsible for the ``decoupling'' of transport properties of supercooled liquids. This result further demonstrates the necessity of a spatial description of the glass formation and therefore seriously challenges a number of popular alternative theoretical descriptions.

cond-mat.stat-mech↗
arXiv2003

Time and length scales in spin glasses

We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three dimensional Heisenberg spin glass.

cond-mat.dis-nn↗
arXiv2003

Reply to Comment on "Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models"

We have recently shown that in non-equilibrium spin systems at criticality the limit $\Xin$ of the fluctuation-dissipation ratio X(t,tw) for t >> tw >> 1 can be measured using observables such as magnetization or energy [Phys. Rev.\ E {\bf 68}, 016116 (2003)]. Pleimling argues in a Comment [cond-mat/0309652] on our paper that for such observables correlation and response functions are dominated by one-time quantities dependent only on t, and are therefore not suitable for a determination of $\Xin$. Using standard scaling forms of correlation and response functions, as used by Pleimling, we show that our data do have a genuine two-time dependence and allow X(t,tw) and $\Xin$ to be measured, so that Pleimling's criticisms are easily refuted. We also compare with predictions from renormalization-group calculations, which are consistent with our numerical observation of a fluctuation-dissipation plot for the magnetization that is very close to a straight line. A key point remains that coherent observables make measurements of $\Xin$ easier than the traditionally used incoherent ones, producing fluctuation-dissipation plots whose slope is close to $\Xin$ over a much larger range.

cond-mat.stat-mech↗
arXiv2003

Real space origin of temperature crossovers in supercooled liquids

We show that the various crossovers between dynamical regimes observed in experiments and simulations of supercooled liquids can be explained in simple terms from the existence and statistical properties of dynamical heterogeneities. We confirm that dynamic heterogeneity is responsible for the slowing down of glass formers at temperatures well above the dynamic singularity T_c predicted by mode coupling theory. Our results imply that activated processes govern the long-time dynamics even in the temperature regime where they are neglected by mode-coupling theory. We show that alternative interpretations based on topographic properties of the potential energy landscape are complicated and inefficient ways of describing simple physical features which are naturally accounted for within our approach. We show in particular that the reported links between mode coupling and landscape singularities do not exist.

cond-mat.stat-mech↗
arXiv2003

Energetics of clusters in the two-dimensional Ising spin glass

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relatively good agreement with standard domain wall calculations.

cond-mat.dis-nn↗
arXiv2003

Non-topographic description of inherent structure dynamics in glass formers

We show that the dynamics between inherent structures in glass forming systems can be understood in purely dynamical terms, without any reference to ``topographic'' features of the potential energy landscape. This ``non-topographic'' interpretation is based instead on the existence of dynamical heterogeneities and on their statistical properties. Our view is supported by the study of simple dynamically facilitated models of glass formers. These models also allow for the formulation of quantitative theoretical predictions which are successfully compared to published data obtained in numerical and experimental studies of local dynamics of supercooled liquids.

cond-mat.stat-mech↗
arXiv2003

A consequence of local equilibration and heterogeneity in glassy materials

The existence of a generalized fluctuation-dissipation theorem observed in simulations and experiments performed in various glassy materials is related to the concepts of local equilibration and heterogeneity in space. Assuming the existence of a dynamic coherence length scale up to which the system is locally equilibrated, we extend previous generalizations of the FDT relating static to dynamic quantities to the physically relevant domain where asymptotic limits of large times and sizes are not reached. The formulation relies on a simple scaling argument and has thus not the character of a theorem. Extensive numerical simulations support this proposition. Our results quite generally apply to systems with slow dynamics, independently of the space dimensionality, the chosen dynamics, or the presence of disorder.

cond-mat.stat-mech↗
arXiv2003

Finite size scaling analysis of the glass transition

We show that finite size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging correlation length at the glass transition whose physical manifestation is the presence of dynamical heterogeneities. We introduce a parameter B(T,L) whose temperature, T, and system size, L, dependences permit a precise location of the glass transition. We discuss the finite size scaling behaviour of a diverging susceptibility χ(L,T). These new techniques are successfully used to study two lattice models. The analysis straightforwardly applies to any glass-forming system.

cond-mat.stat-mech↗
arXiv2003

Fluctuation-dissipation relations in the non-equilibrium critical dynamics of Ising models

We investigate the relation between two-time, multi-spin, correlation and response functions in the non-equilibrium critical dynamics of Ising models in d=1 and d=2 spatial dimensions. In these non-equilibrium situations, the fluctuation-dissipation theorem (FDT) is not satisfied. We find FDT `violations' qualitatively similar to those reported in various glassy materials, but quantitatively dependent on the chosen observable, in contrast to the results obtained in infinite-range glass models. Nevertheless, all FDT violations can be understood by considering separately the contributions from large wavevectors, which are at quasi-equilibrium and obey FDT, and from small wavevectors where a generalized FDT holds with a non-trivial limit fluctuation-dissipation ratio X. In d=1, we get X = 1/2 for spin observables, which measure the orientation of domains, while X = 0 for observables that are sensitive to the domain-wall motion. Numerical simulations in d=2 reveal a unique X = 0.34 for all observables. Measurement protocols for X are discussed in detail. Our results suggest that the definition of an effective temperature Teff = T / X for large length scales is generically possible in non-equilibrium critical dynamics.

cond-mat.stat-mech↗
arXiv2002

Hiking through glassy phases: physics beyond aging

Experiments performed on a wide range of glassy materials display many interesting phenomena, such as aging behavior. In recent years, a large body of experiments probed this nonequilibrium glassy dynamics through elaborate protocols, in which external parameters are shifted, or cycled in the course of the experiment. We review here these protocols, as well as experimental and numerical results. Then, we critically discuss various theoretical approaches put forward in this context. Emphasis is put more on the generality of the phenomena than on a specific system. Experiments are also suggested.

cond-mat.stat-mech↗
arXiv2002

Yield stress, heterogeneities and activated processes in soft glassy materials

The rheological behavior of soft glassy materials basically results from the interplay between shearing forces and an intrinsic slow dynamics. This competition can be described by a microscopic theory, which can be viewed as a nonequilibrium schematic mode-coupling theory. This statistical mechanics approach to rheology results in a series of detailed theoretical predictions, some of which still awaiting for their experimental verification. We present new, preliminary, results about the description of yield stress, flow heterogeneities and activated processes within this theoretical framework.

cond-mat.stat-mech↗
arXiv2002

Geometrical Aspects of Aging and Rejuvenation in the Ising Spin Glass: A Numerical Study

We present a comprehensive study of non-equilibrium phenomena in the low temperature phase of the Edwards-Anderson Gaussian spin glass in 3 and 4 spatial dimensions. Many effects can be understood in terms of a time dependent coherence length, $\ell_T$, such that length scales smaller that $\ell_T$ are equilibrated, whereas larger length scales are essentially frozen. The time and temperature dependence of $\ell_T$ is found to be compatible with critical power-law dynamical scaling for small times/high temperatures, crossing over to an activated logarithmic growth for longer times/lower temperatures, in agreement with recent experimental results. The activated regime is governed by a `barrier exponent' psi which we estimate to be psi ~ 1.0 and psi ~ 2.3 in 3 and 4 dimensions, respectively. We observe for the first time the rejuvenation and memory effects in the four dimensional sample, which, we argue, is unrelated to `temperature chaos'. Our discussion in terms of length scales allows us to address several experimentally relevant issues, such as super-aging versus sub-aging effects, the role of a finite cooling rate, or the so-called Kovacs effect.

cond-mat.stat-mech↗
arXiv2002

Shearing a Glassy Material: Numerical Tests of Nonequilibrium Mode-Coupling Approaches and Experimental Proposals

The predictions of a nonequilibrium schematic mode-coupling theory developed to describe the nonlinear rheology of soft glassy materials have been numerically challenged in a sheared binary Lennard-Jones mixture. The theory gives an excellent description of the stress/temperature `jamming phase diagram' of the system. In the present paper, we focus on the issue of an effective temperature Teff for the slow modes of the fluid, as defined from a generalized fluctuation-dissipation theorem. As predicted theoretically, many different observables are found to lead to the same value of Teff, suggesting several experimental procedures to measure Teff. New, simple experimental protocols to access Teff from a generalized equipartition theorem are also proposed, and one such experiment is numerically performed. These results give strong support to the thermodynamic interpretation of Teff and make it experimentally accessible in a very direct way.

cond-mat.stat-mech↗
arXiv2002

Surfing on a critical line: Rejuvenation without chaos, Memory without a hierarchical phase space

The dynamic behaviour of glassy materials displays strong nonequilibrium effects, such as ageing in simple protocols, memory, rejuvenation and Kovacs effects in more elaborated experiments. We show that this phenomenology may be easily understood in the context of the nonequilibrium critical dynamics of non-disordered systems, the main ingredient being the existence of an infinite equilibrium correlation length. As an example, we analytically investigate the behaviour of the 2D XY model submitted to temperature protocols similar to experiments. This shows that typical glassy effects may be obtained by `surfing on a critical line' without invoking the concept of temperature chaos nor the existence of a hierarchical phase space, as opposed to previous theoretical approaches. The relevance of this phenomenological approach to glassy dynamics is finally discussed.

cond-mat.stat-mech↗
arXiv2002

Nonequilibrium dynamics and fluctuation-dissipation relation in a sheared fluid

The nonequilibrium dynamics of a binary Lennard-Jones mixture in a simple shear flow is investigated by means of molecular dynamics simulations. The range of temperature investigated covers both the liquid, supercooled and glassy states, while the shear rate covers both the linear and nonlinear regimes of rheology. The results can be interpreted in the context of a nonequilibrium, schematic mode-coupling theory developed recently, which makes the theory applicable to a wide range of soft glassy materials. The behavior of the viscosity is first investigated. In the nonlinear regime, strong shear-thinning is obtained. Scaling properties of the intermediate scattering functions are studied. Standard `mode-coupling properties' of factorization and time-superposition hold in this nonequilibrium situation. The fluctuation-dissipation relation is violated in the shear flow in a way very similar to that predicted theoretically, allowing for the definition of an effective temperature Teff for the slow modes of the fluid. Temperature and shear rate dependencies of Teff are studied using density fluctuations as an observable. The observable dependence of Teff is also investigated. Many different observables are found to lead to the same value of Teff, suggesting several experimental procedures to access Teff. It is proposed that tracer particle of large mass may play the role of an `effective thermometer'. When the Einstein frequency of the tracers becomes smaller than the inverse relaxation time of the fluid, a nonequilibrium equipartition theorem holds. This last result gives strong support to the thermodynamic interpretation of Teff and makes it experimentally accessible in a very direct way.

cond-mat.soft↗
arXiv2001

Real space application of the mean-field description of spin glass dynamics

The out of equilibrium dynamics of finite dimensional spin glasses is considered from a point of view going beyond the standard `mean-field theory' versus `droplet picture' debate of the last decades. The main predictions of both theories concerning the spin glass dynamics are discussed. It is shown, in particular, that predictions originating from mean-field ideas concerning the violations of the fluctuation-dissipation theorem apply quantitatively, provided one properly takes into account the role of the spin glass coherence length which plays a central role in the droplet picture. Dynamics in a uniform magnetic field is also briefly discussed.

cond-mat.stat-mech↗