arXiv subjects

Gilles Tarjus

Publications and source records attributed to Gilles Tarjus.

At least 73 records · Page 4Linked to original sources

arXiv2012

Geometrical Frustration and Static Correlations in a Simple Glass Former

We study the geometrical frustration scenario of glass formation for simple hard sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing down of relaxation, because of the strong frustration characterizing these systems. The possibility of a growing static length is furthermore found to be physically irrelevant in the regime that is accessible to computer simulations.

cond-mat.dis-nn↗

arXiv2011

Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance

We reformulate the nonperturbative functional renormalization group for the random field Ising model in a superfield formalism, extending the supersymmetric description of the critical behavior of the system first proposed by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)]. We show that the two crucial ingredients for this extension are the introduction of a weighting factor, which accounts for ground-state dominance when multiple metastable states are present, and of multiple copies of the original system, which allows one to access the full functional dependence of the cumulants of the renormalized disorder and to describe rare events. We then derive exact renormalization group equations for the flow of the renormalized cumulants associated with the effective average action.

cond-mat.stat-mech↗

arXiv2011

Nonperturbative Functional Renormalization Group for Random Field Models. IV: Supersymmetry and its spontaneous breaking

We apply the nonperturbative functional renormalization group (NP-FRG) in the superfield formalism that we have developed in the preceding paper to study long-standing issues concerning the critical behavior of the random field Ising model. Through the introduction of an appropriate regulator and a supersymmetry-compatible nonperturbative approximation, we are able to follow the supersymmetry, more specifically the superrotational invariance first unveiled by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)], and its spontaneous breaking along the RG flow. Breaking occurs below a critical dimension dDR \simeq 5.1, and the supersymmetry-broken fixed point that controls the critical behavior then leads to a breakdown of the "dimensional reduction" property. We solve the NP-FRG flow equations numerically and determine the critical exponents as a function of dimension down to d < 3, with a good agreement in d = 3 and d = 4 with the existing numerical estimates.

cond-mat.stat-mech↗

arXiv2011

Testing "microscopic" theories of glass-forming liquids

We assess the validity of "microscopic" approaches of glass-forming liquids based on the sole k nowledge of the static pair density correlations. To do so we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while disp laying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhausti ve, and we have not tested the effect of adding corrections by including for instance three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowd own of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by "microscopic" appr oaches only requiring the static pair density correlations as nontrivial input.

cond-mat.stat-mech↗

arXiv2011

Supersymmetry and its spontaneous breaking in the random field Ising model

We provide a resolution of one of the long-standing puzzles in the theory of disordered systems. By reformulating the functional renormalization group (FRG) for the critical behavior of the random field Ising model in a superfield formalism, we are able to follow the associated supersymmetry and its spontaneous breaking along the FRG flow. Breaking is shown to occur below a critical dimension $d_{DR}\simeq 5.1$ and leads to a breakdown of the "dimensional reduction" property. We compute the critical exponents as a function of dimension and give evidence that scaling is described by three independent exponents.

cond-mat.stat-mech↗

arXiv2011

Hierarchical Reference Theory of critical fluids in disordered porous media

We consider the equilibrium behavior of fluids imbibed in disordered mesoporous media, including their gas-liquid critical point when present. Our starting points are on the one hand a description of the fluid/solid-matrix system as a quenched-annealed mixture and on the other hand the Hierarchical Reference Theory (HRT) developed by A. Parola and L. Reatto to cope with density fluctuations on all length scales. The formalism combines liquid-state statistical mechanics and the theory of systems in the presence of quenched disorder. A straightforward implementation of the HRT to the quenched-annealed mixture is shown to lead to unsatisfactory results, while indicating that the critical behavior of the system is in the same universality class as that of the random-field Ising model. After a detour via the field-theoretical renormalization group approach of the latter model, we finally lay out the foundations for a proper HRT of fluids in a disordered porous material.

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arXiv2011

The role of attractive forces in viscous liquids

We present evidence from computer simulation that the slowdown of relaxation of a standard Lennard-Jones glass-forming liquid and that of its reduction to a model with truncated pair potentials without attractive tails is quantitatively and qualitatively different in the viscous regime. The pair structure of the two models is however very similar. This finding, which appears to contradict the common view that the physics of dense liquids is dominated by the steep repulsive forces between atoms, is characterized in detail, and its consequences are explored. Beyond the role of attractive forces themselves, a key aspect in explaining the differences in the dynamical behavior of the two models is the truncation of the interaction potentials beyond a cutoff at typical interatomic distance. This leads us to question the ability of the jamming scenario to describe the physics of glass-forming liquids and polymers.

cond-mat.stat-mech↗

arXiv2010

An overview of the theories of the glass transition

The topic of the glass transition gives rise to a a wide diversity of views. It is, accordingly, characterized by a lack of agreement on which would be the most profitable theoretical perspective. In this chapter, I provide some elements that can help sorting out the many theoretical approaches, understanding their foundations, as well as discussing their validity and mutual compatibility. Along the way, I describe the progress made in the last twenty years, including new insights concerning the spatial heterogeneity of the dynamics and the characteristic length scales associated with the glass transition. An emphasis is put on those theories that associate glass formation with growing collective behavior and emerging universality.

cond-mat.stat-mech↗

arXiv2010

Renormalization group analysis of the random first order transition

We consider the approach describing glass formation in liquids as a progressive trapping in an exponentially large number of metastable states. To go beyond the mean-field setting, we provide a real-space renormalization group (RG) analysis of the associated replica free-energy functional. The present approximation yields in finite dimensions an ideal glass transition similar to that found in mean field. However, we find that along the RG flow the properties associated with metastable glassy states, such as the configurational entropy, are only defined up to a characteristic length scale that diverges as one approaches the ideal glass transition. The critical exponents characterizing the vicinity of the transition are the usual ones associated with a first-order discontinuity fixed point.

cond-mat.dis-nn↗

arXiv2010

Statistical Mechanics of liquids and fluids in curved space

In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter on the phase behavior, thermodynamics and structure of simple liquids. Reference will also be made to existing work on three-dimensional curved space and two-dimensional manifolds with varying curvature.

cond-mat.stat-mech↗

arXiv2010

A critical test of the mode-coupling theory of the glass transition

The mode-coupling theory of the glass transition predicts the time evolution of the intermediate scattering functions in viscous liquids on the sole basis of the structural information encoded in two-point density correlations. We provide a critical test of this property and show that the theory fails to describe the qualitatively distinct dynamical behavior obtained in two model liquids characterized by very similar pair correlation functions. Because we use `exact' static information provided by numerical simulations, our results are a direct proof that some important information about the dynamics of viscous liquids is not captured by pair correlations, and is thus not described by the mode-coupling theory, even in the temperature regime where the theory is usually applied.

cond-mat.stat-mech↗

arXiv2010

Structure and dynamics of topological defects in a glassy liquid on a negatively curved manifold

We study the low-temperature regime of an atomic liquid on the hyperbolic plane by means of molecular dynamics simulation and we compare the results to a continuum theory of defects in a negatively curved hexagonal background. In agreement with the theory and previous results on positively curved (spherical) surfaces, we find that the atomic configurations consist of isolated defect structures, dubbed "grain boundary scars", that form around an irreducible density of curvature-induced disclinations in an otherwise hexagonal background. We investigate the structure and the dynamics of these grain boundary scars.

cond-mat.stat-mech↗

arXiv2010

Growing static and dynamic length scales in a glass-forming liquid

We investigate the characteristic length scales associated with the glass transition phenomenon. By studying an atomic glass-forming liquid in negatively curved space, for which the local order is well identified and the amount of frustration opposing the spatial extension of this order is tunable, we provide insight into the structural origin of the main characteristics of the dynamics leading to glass formation. We find that the structural length and the correlation length characterizing the increasing heterogeneity of the dynamics grow together as temperature decreases. However, the system eventually enters a regime in which the former saturates as a result of frustration whereas dynamic correlations keep building up.

cond-mat.stat-mech↗

arXiv2009

Bootstrap percolation and kinetically constrained models on hyperbolic lattices

We study bootstrap percolation (BP) on hyperbolic lattices obtained by regular tilings of the hyperbolic plane. Our work is motivated by the connection between the BP transition and the dynamical transition of kinetically constrained models, which are in turn relevant for the study of glass and jamming transitions. We show that for generic tilings there exists a BP transition at a nontrivial critical density, $0<ρ_c<1$. Thus, despite the presence of loops on all length scales in hyperbolic lattices, the behavior is very different from that on Euclidean lattices where the critical density is either zero or one. Furthermore, we show that the transition has a mixed character since it is discontinuous but characterized by a diverging correlation length, similarly to what happens on Bethe lattices and random graphs of constant connectivity.

cond-mat.stat-mech↗

arXiv2009

Nonperturbative effect of attractive forces in viscous liquids

We study the role of the attractive intermolecular forces in the viscous regime of a simple glass-forming liquid by using computer simulations. To this end, we compare the structure and the dynamics of a standard Lennard-Jones glass-forming liquid model with and without the attractive tail of the interaction potentials. The viscous slowing down of the two systems are found to be quantitatively and qualitatively different over a broad density range, whereas the static pair correlations remain close. The common assumption that the behaviour of dense nonassociated liquids is determined by the short-ranged repulsive part of the intermolecular potentials dramatically breaks down for the relaxation in the viscous liquid regime.

cond-mat.stat-mech↗

arXiv2009

Thermodynamics and structure of simple liquids in the hyperbolic plane

We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk thermodynamic pressure to the pair correlation function and we develop the appropriate setting for extending the integral-equation approach of liquid-state theory in order to describe the fluid structure. We apply the formalism and study the influence of negative space curvature on two types of systems that have been recently considered: Coulombic systems, such as the one- and two-component plasma models, and fluids interacting through short-range pair potentials, such as the hard-disk and the Lennard-Jones models.

cond-mat.stat-mech↗

arXiv2008

Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane

We study by Molecular Dynamics simulation the slowing down of particle motion in a two-dimensional monatomic model: a Lennard-Jones liquid on the hyperbolic plane. The negative curvature of the embedding space frustrates the long-range extension of the local hexagonal order. As a result, the liquid avoids crystallization and forms a glass. We show that, as temperature decreases, the single particle motion displays the canonical features seen in real glassforming liquids: the emergence of a "plateau" at intermediate times in the mean square displacement and a decoupling between the local relaxation time and the (hyperbolic) diffusion constant.

cond-mat.stat-mech↗

arXiv2008

Tuning the fragility of a glassforming liquid by curving space

We investigate the influence of space curvature, and of the associated "frustration", on the dynamics of a model glassformer: a monatomic liquid on the hyperbolic plane. We find that the system's fragility, i.e. the sensitivity of the relaxation time to temperature changes, increases as one decreases the frustration. As a result, curving space provides a way to tune fragility and make it as large as wanted. We also show that the nature of the emerging "dynamic heterogeneities", another distinctive feature of slowly relaxing systems, is directly connected to the presence of frustration-induced topological defects.

cond-mat.stat-mech↗