arXiv subjects

Ludovic Berthier

Publications and source records attributed to Ludovic Berthier.

At least 55 records · Page 3Linked to original sources

arXiv2023

Front propagation in ultrastable glasses is dynamically heterogeneous

Upon heating, ultrastable glassy films transform into liquids via a propagating equilibration front, resembling the heterogeneous melting of crystals. A microscopic understanding of this robust phenomenology is however lacking because experimental resolution is limited. We simulate the heterogeneous transformation kinetics of ultrastable configurations prepared using the swap Monte Carlo algorithm, thus allowing direct comparison with experiments. We resolve the liquid-glass interface both in space and time as well as the underlying particle motion responsible for its propagation. We perform a detailed statistical analysis of the interface geometry and kinetics over a broad range of temperatures. We show that the dynamic heterogeneity of the bulk liquid is passed on to the front which propagates heterogeneously in space and intermittently in time. This observation allows us to relate the averaged front velocity to the equilibrium diffusion coefficient of the liquid. We suggest that an experimental characterisation of the interface geometry during the heterogeneous devitrification of ultrastable glassy films would provide direct experimental access to the long-sought characteristic lengthscale of dynamic heterogeneity in bulk supercooled liquids.

cond-mat.stat-mech↗

arXiv2023

Modern computational studies of the glass transition

The physics of the glass transition and amorphous materials continues to attract the attention of a wide research community after decades of effort. Supercooled liquids and glasses have been studied numerically since the advent of molecular dynamics and Monte Carlo simulations in the last century. Computer studies have greatly enhanced both experimental discoveries and theoretical developments and constitute an active and continually expanding research field. Our goal in this review is to provide a modern perspective on this area. We describe the need to go beyond canonical methods to attack a problem that is notoriously difficult in terms of time scales, length scales, and physical observables. We first summarise recent algorithmic developments to achieve enhanced sampling and faster equilibration using replica exchange methods, cluster and swap Monte Carlo algorithms, and other techniques. We then review some major recent advances afforded by these novel tools regarding the statistical mechanical description of the liquid-to-glass transition as well as the mechanical, vibrational and thermal properties of the glassy solid. We finally describe some important challenges for future research.

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arXiv2023

Microscopic observation of two-level systems in a metallic glass model

The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements.

cond-mat.dis-nn↗

arXiv2023

Two-step devitrification of ultrastable glasses

The discovery of ultrastable glasses has raised novel challenges about glassy systems. Recent experiments studied the macroscopic devitrification of ultrastable glasses into liquids upon heating but lacked microscopic resolution. We use molecular dynamics simulations to analyse the kinetics of this transformation. In the most stable systems, devitrification occurs after a very large time, but the liquid emerges in two steps. At short times, we observe the rare nucleation and slow growth of isolated droplets containing a liquid maintained under pressure by the rigidity of the surrounding glass. At large times, pressure is released after the droplets coalesce into large domains, which accelerates devitrification. This two-step process produces pronounced deviations from the classical Avrami kinetics and explains the emergence of a giant lengthscale characterising the devitrification of bulk ultrastable glasses. Our study elucidates the nonequilibrium kinetics of glasses following a large temperature jump, which differs from both equilibrium relaxation and aging dynamics, and will guide future experimental studies.

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arXiv2022

Thirty milliseconds in the life of a supercooled liquid

We combine the swap Monte Carlo algorithm to long multi-CPU molecular dynamics simulations to analyse the equilibrium relaxation dynamics of model supercooled liquids over a time window covering ten orders of magnitude for temperatures down to the experimental glass transition temperature $T_g$. The analysis of \rev{several} time correlation functions coupled to spatio-temporal resolution of particle motion allow us to elucidate the nature of the equilibrium dynamics in deeply supercooled liquids. We find that structural relaxation starts at early times in rare localised regions characterised by a waiting time distribution that develops a power law near $T_g$. At longer times, relaxation events accumulate with increasing probability in these regions as $T_g$ is approached. This accumulation leads to a power-law growth of the linear extension of relaxed domains with time with a large, temperature-dependent dynamic exponent. Past the average relaxation time, unrelaxed domains slowly shrink with time due to relaxation events happening at their boundaries. Our results provide a complete microscopic description of the particle motion responsible for key experimental signatures of glassy dynamics, from the shape and temperature evolution of relaxation spectra to the core features of dynamic heterogeneity. They also provide a microscopic basis to understand the emergence of dynamic facilitation in deeply supercooled liquids and allow us to critically reassess theoretical descriptions of the glass transition.

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arXiv2022

Computer simulations of the glass transition and glassy materials

We provide an overview of the different types of computational techniques developed over the years to study supercooled liquids, glassy materials and the physics of the glass transition. We organise these numerical strategies into four broad families. For each of them, we describe the general ideas without discussing any technical details. We summarise the type of questions which can be addressed by any given approach and outline the main results which have been obtained. Finally we describe two important directions for future computational studies of glassy systems.

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arXiv2022

Is glass a state of matter?

Glass is everywhere. We use and are surrounded by glass objects which make tangible the reality of glass as a distinct state of matter. Yet, glass as we know it is usually obtained by cooling a liquid sufficiently rapidly below its melting point to avoid crystallisation. The viscosity of this supercooled liquid increases by many orders of magnitude upon cooling, until the liquid becomes essentially arrested on experimental timescales below the ``glass transition'' temperature. From a structural viewpoint, the obtained glass still very much resembles the disordered liquid, but from a mechanical viewpoint, it is as rigid as an ordered crystal. Does glass qualify as a separate state of matter? We provide a pedagogical perspective on this question using basic statistical mechanical concepts. We recall the definitions of states of matter and of phase transitions between them. We review recent theoretical results suggesting why and how an ``ideal glass'' can indeed be defined as a separate equilibrium state of matter. We discuss recent success of computer simulations trying to analyse this glass state. We close with some experimental perspectives.

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arXiv2022

Rare events and disorder control the brittle yielding of well-annealed amorphous solids

We use atomistic computer simulations to provide a microscopic description of the brittle failure of amorphous materials, and we assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions, similarly to Griffiths effects in disordered systems. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band. This physical picture, which no longer holds in poorly annealed ductile materials, allows us to discuss the role of finite size effects in brittle yielding and reinforces the similarities between yielding and other disorder-controlled nonequilibrium phase transitions.

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arXiv2022

Collective dynamics in a glass-former with Mari-Kurchan interactions

We numerically study the equilibrium relaxation dynamics of a two-dimensional Mari-Kurchan glass model. The tree-like structure of particle interactions forbids both non-trivial structural motifs and the emergence of a complex free-energy landscape leading to a thermodynamic glass transition, while the finite-dimensional nature of the model prevents the existence of a mode-coupling singularity. Nevertheless, the equilibrium relaxation dynamics is shown to be in excellent agreement with simulations performed in conventional glass-formers. Averaged time-correlation functions display a phenomenology typical of supercooled liquids, including the emergence of an excess signal in relaxation spectra at intermediate frequencies. We show that this evolution is accompanied by strong signatures of collective and heterogeneous dynamics which cannot be interpreted in terms of single particle hopping and emerge from dynamic facilitation. Our study demonstrates that an off-lattice interacting particle model with extremely simple structural correlations displays quantitatively realistic glassy dynamics.

cond-mat.dis-nn↗

arXiv2022

Disordered collective motion in dense assemblies of persistent particles

We explore the emergence of nonequilibrium collective motion in disordered non-thermal active matter when persistent motion and crowding effects compete, using simulations of a two-dimensional model of size polydisperse self-propelled particles. In stark contrast with monodisperse systems, we find that polydispersity stabilizes a homogeneous active liquid at arbitrary large persistence times, characterized by remarkable velocity correlations and irregular turbulent flows. For all persistence values, the active fluid undergoes a nonequilibrium glass transition at large density. This is accompanied by collective motion, whose nature evolves from near-equilibrium spatially heterogeneous dynamics at small persistence, to a qualitatively different intermittent dynamics when persistence is large. This latter regime involves a complex time evolution of the correlated displacement field

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arXiv2022

Microscopic origin of excess wings in relaxation spectra of supercooled liquids

Glass formation is encountered in diverse materials. Experiments have revealed that dynamic relaxation spectra of supercooled liquids generically become asymmetric near the glass transition temperature, $T_g$, where an extended power law emerges at high frequencies. The microscopic origin of this "wing" remains unknown, and was so far inaccessible to simulations. Here, we develop a novel computational approach and study the equilibrium dynamics of model supercooled liquids near $T_g$. We demonstrate the emergence of a power law wing in numerical spectra, which originates from relaxation at rare, localised regions over broadly-distributed timescales. We rationalise the asymmetric shape of relaxation spectra by constructing an empirical model associating heterogeneous activated dynamics with dynamic facilitation, which are the two minimal physical ingredients revealed by our simulations. Our work offers a glimpse of the molecular motion responsible for glass formation at relevant experimental conditions.

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arXiv2022

Static self-induced heterogeneity in glass-forming liquids: Overlap as a microscope

We propose and numerically implement a local probe of the static self-induced heterogeneity characterizing glass-forming liquids. The method relies on the equilibrium statistics of the overlap between pairs of configurations measured in mesoscopic cavities with unconstrained boundaries. By systematically changing the location of the probed cavity, we directly detect spatial variations of the overlap fluctuations. We provide a detailed analysis of the statistics of a local estimate of the configurational entropy and we infer an estimate of the surface tension between amorphous states, ingredients that are both at the basis of the random first-order transition theory of glass formation. Our results represent the first direct attempt to visualize and quantify the self-induced heterogeneity underpinning the thermodynamics of glass formation. They pave the way for the development of coarse-grained effective theories and for a direct assessment of the role of thermodynamics in the activated dynamics of deeply supercooled liquids.

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arXiv2022

Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice

We present numerical tests of the fluctuation-dissipation theorem (FDT) in the dumbbell model of spin ice with parameters suitable for dysprosium titanate. The tests are made for local spin variables, magnetic monopole density, and energy. We are able to achieve local equilibrium in which the FDT is satisfied down to $T=0.4$ K below which the system completely freezes. Non-equilibrium dynamics, together with violation of the FDT, are nonetheless observed following a thermal quench into the non-contractable monopole pair regime. Despite FDT violation, an approximate linear response regime allows for the identification of effective non-equilibrium temperatures which are different for each variable. The spin variable appears hotter than the heat reservoir, the monopole concentration responds with a lower effective temperature while the energy has a negative effective temperature. Results are discussed in the context of the monopole picture of spin ice and compared to the structure of FDT violations in other glassy materials. Prospectives for future experiments are reviewed.

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arXiv2022

Relaxation dynamics in the energy landscape of glass-forming liquids

We numerically study the zero-temperature relaxation dynamics of several glass-forming models to their inherent structures, following quenches from equilibrium configurations sampled across a wide range of initial temperatures. In a mean-field Mari-Kurchan model, we find that relaxation changes from a power-law to an exponential decay below a well-defined temperature, consistent with recent findings in mean-field $p$-spin models. By contrast, for finite-dimensional systems, the relaxation is always algebraic, with a non-trivial universal exponent at high temperatures crossing over to a harmonic value at low temperatures. We demonstrate that this apparent evolution is controlled by a temperature-dependent population of localised glassy excitations. Our work unifies several recent lines of studies aiming at a detailed characterisation of the complex potential energy landscape of glass-formers, and challenges both mean-field and real space descriptions of glasses.

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arXiv2022

Statistical mechanics of coupled supercooled liquids in finite dimensions

We study the statistical mechanics of supercooled liquids when the system evolves at a temperature $T$ with a field $ε$ linearly coupled to its overlap with a reference configuration of the same liquid sampled at a temperature $T_0$. We use mean-field theory to fully characterize the influence of the reference temperature $T_0$, and we mainly study the case of a fixed, low-$T_0$ value in computer simulations. We numerically investigate the extended phase diagram in the $(ε,T)$ plane of model glass-forming liquids in spatial dimensions $d=2$ and $d=3$, relying on umbrella sampling and reweighting techniques. For both $2d$ and $3d$ cases, a similar phenomenology with nontrivial thermodynamic fluctuations of the overlap is observed at low temperatures, but a detailed finite-size analysis reveals qualitatively distinct behaviors. We establish the existence of a first-order transition line for nonzero $ε$ ending in a critical point in the universality class of the random-field Ising model (RFIM) in $d=3$. In $d=2$ instead, no phase transition is found in large enough systems at least down to temperatures below the extrapolated calorimetric glass transition temperature $T_g$. Our results confirm that glass-forming liquid samples of limited size display the thermodynamic fluctuations expected for finite systems undergoing a random first-order transition. They also support the relevance of the physics of the RFIM for supercooled liquids, which may then explain the qualitative difference between $2d$ and $3d$ glass-formers.

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arXiv2021

Excess wings and asymmetric relaxation spectra in a facilitated trap model

In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally-activated dynamics of glassy systems. We fully characterise the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the strength of dynamic facilitation, combining numerical results and analytic arguments. Dynamic facilitation generically accelerates the relaxation of the deepest traps, thus making relaxation spectra strongly asymmetric, with an apparent "excess" signal at high frequencies. For well-chosen values of the parameters, the obtained spectra mimic experimental results for organic liquids displaying an excess wing. Overall, our results identify the minimal physical ingredients needed to describe excess processes in relaxation spectra of supercooled liquids.

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arXiv2021

Self-induced heterogeneity in deeply supercooled liquids

A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecule studies. Surprisingly broad thermodynamic fluctuations are also found, which correlate well with dynamics fluctuations, thus providing a local test of the thermodynamic origin of slow dynamics.

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arXiv2021

Relaxation dynamics of non-Brownian spheres below jamming

We numerically study the relaxation dynamics and associated criticality of non-Brownian frictionless spheres below jamming in spatial dimensions $d=2$, $3$, $4$, and $8$, and in the mean-field Mari-Kurchan model. We discover non-trivial finite-size and volume fraction dependences of the relaxation time associated to the relaxation of unjammed packings. In particular, the relaxation time is shown to diverge logarithmically with system size at any density below jamming, and no critical exponent can characterise its behaviour approaching jamming. In mean-field, the relaxation time is instead well-defined: it diverges at jamming with a critical exponent that we determine numerically and differs from an earlier mean-field prediction. We rationalise the finite $d$ logarithmic divergence using an extreme-value statistics argument in which the relaxation time is dominated by the most connected region of the system. The same argument shows that the earlier proposition that relaxation dynamics and shear viscosity are directly related breaks down in large systems. The shear viscosity of non-Brownian packings is well-defined in all $d$ in the thermodynamic limit, but large finite-size effects plague its measurement close to jamming.

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