arXiv subjects

Gilles Tarjus

Publications and source records attributed to Gilles Tarjus.

At least 55 records · Page 3Linked to original sources

arXiv2015

Avalanches and perturbation theory in the random-field Ising model

Perturbation theory for the random-field Ising model (RFIM) has the infamous attribute that it predicts at all orders a dimensional-reduction property for the critical behavior that turns out to be wrong in low dimension. Guided by our previous work based on the nonperturbative functional renormalization group (NP-FRG), we show that one can still make some use of the perturbation theory for a finite range of dimension below the upper critical dimension, d=6. The new twist is to account for the influence of large-scale zero-temperature events known as avalanches. These avalanches induce nonanalyticities in the field dependence of the correlation functions and renormalized vertices, and we compute in a loop expansion the eigenvalue associated with the corresponding anomalous operator. The outcome confirms the NP-FRG prediction that the dimensional-reduction fixed point correctly describes the dominant critical scaling of the RFIM above some dimension close to 5 but not below.

cond-mat.dis-nn↗

arXiv2015

Nonperturbative fluctuations and metastability in a simple model: from observables to microscopic theory and back

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 mean-field level. To gain insight into such hard problems, we consider the implementation of a generic back-and-forth 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 one-dimensional $φ^4$ 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 finite-size 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.

cond-mat.stat-mech↗

arXiv2015

Mode-coupling approach for the slow dynamics of a liquid on a spherical substrate

We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have derived the MCT equations in a spherical geometry. We find that, as seen from the MCT, the slow dynamics of liquids in curved space at low temperature does not qualitatively differ from that of glass-forming liquids in Euclidean space. The MCT predicts the right trend for the evolution of the relaxation slowdown with curvature but is dramatically off at a quantitative level.

cond-mat.soft↗

arXiv2015

Activated dynamic scaling in the random-field Ising model: a nonperturbative functional renormalization group approach

The random-field Ising model shows extreme critical slowdown that has been described by activated dynamic scaling: the characteristic time for the relaxation to equilibrium diverges exponentially with the correlation length, $\ln τ\sim ξ^ψ/T$ , with $ψ$ an \textit{a priori} unknown barrier exponent. Through a nonperturbative functional renormalization group, we show that for spatial dimensions $d$ less than a critical value $d_{DR} \simeq 5.1$, also associated with dimensional-reduction breakdown, $ψ=θ$ with $θ$ the temperature exponent near the zero-temperature fixed point that controls the critical behavior. For $d>d_{DR}$ on the other hand, $ψ=θ-2λ$ where $θ=2$ and $λ>0$ a new exponent. At the upper critical dimension $d=6$, $λ=1$ so that $ψ=0$, and activated scaling gives way to conventional scaling. We give a physical interpretation of the results in terms of collective events in real space, avalanches and droplets. We also propose a way to check the two regimes by computer simulations of long-range 1-$d$ systems.

cond-mat.stat-mech↗

arXiv2015

In search of a theory of supercooled liquids

Despite the absence of consensus on a theory of the transition from supercooled liquids to glasses, the experimental observations suggest that a detail-independent theory should exist.

cond-mat.stat-mech↗

arXiv2014

Critical behavior of the random-field Ising model with long-range interactions in one dimension

We study the critical behavior of the one-dimensional random field Ising model (RFIM) with long-range interactions ($\propto r^{-(d+σ)}$) by the nonperturbative functional renormalization group. We find two distinct regimes of critical behavior as a function of $σ$, separated by a critical value $σ_c$. What distinguishes these two regimes is the presence or not of a cusp-like nonanalyticity in the functional dependence of the renormalized cumulants of the random field at the fixed point. This change of behavior can be associated to the characteristics of the large-scale avalanches present in the system at zero temperature. We propose ways to check these predictions through lattice simulations. We also discuss the difference with the RFIM on the Dyson hierarchical lattice.

cond-mat.stat-mech↗

arXiv2014

Influence of system size on the properties of a fluid adsorbed in a nanopore: Physical manifestations and methodological consequences

We consider the theoretical description of a fluid adsorbed in a nanopore. Hysteresis and discontinuities in the isotherms in general hampers the determination of equilibrium thermodynamic properties, even in computer simulations. A proposed way around this has been to consider both a reservoir of small size and a pore of small extent in order to restrict the fluctuations of density and approach a classical van der Waals loop. We assess this suggestion by thoroughly studying through density functional theory and Monte Carlo simulations the influence of system size on the equilibrium configurations of the adsorbed fluid and on the resulting isotherms. We stress the importance of pore-symmetry-breaking states that even for modest pore sizes lead to discontinuous isotherms and we discuss the physical relevance of these states and the methodological consequences for computing thermodynamic quantities.

cond-mat.soft↗

arXiv2014

Dynamics of a monodisperse Lennard-Jones system on a sphere

We investigate by Molecular Dynamics simulation a system of $N$ particles moving on the surface of a two-dimensional sphere and interacting by a Lennard-Jones potential. We detail the way to account for the changes brought by a nonzero curvature, both at a methodological and at a physical level. When compared to a two-dimensional Lennard-Jones liquid on the Euclidean plane, where a phase transition to an ordered hexagonal phase takes place, we find that the presence of excess defects imposed by the topology of the sphere frustrates the hexagonal order. We observe at high density a rapid increase of the relaxation time when the temperature is decreased, whereas in the same range of temperature the pair correlation function of the system evolves only moderately.

cond-mat.stat-mech↗

arXiv2014

An assessment of the concept of fragility

The concept of "fragility", which was introduced to characterize the degree of super-Arrhenius temperature dependence of the relaxation time and transport coefficients, has since been taken as a key quantity that seems to correlate with other properties of glass-forming liquids and polymers. With the goal of assessing the usefulness and the robustness of the concept, we address here several questions: How to best quantify fragility? How significant are the observed differences in fragility? Is fragility connected to "cooperativity" and collective behavior?

cond-mat.stat-mech↗

arXiv2013

Fixed points and their stability in the functional renormalization group of random field models

We consider the zero-temperature fixed points controlling the critical behavior of the $d$-dimensional random-field Ising, and more generally $O(N)$, models. We clarify the nature of these fixed points and their stability in the region of the $(N,d)$ plane where one passes from a critical behavior satisfying the $d\rightarrow d-2$ dimensional reduction to one where it breaks down due to the appearance of strong enough nonanalyticities in the functional dependence of the cumulants of the renormalized disorder. We unveil an intricate and unusual behavior.

cond-mat.dis-nn↗

arXiv2013

Random-field-like criticality in glass-forming liquids

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.

cond-mat.dis-nn↗

arXiv2013

Morphology transition at depinning in a solvable model of interface growth in a random medium

We propose a simple, exactly solvable, model of interface growth in a random medium that is a variant of the zero-temperature random-field Ising model on the Cayley tree. This model is shown to have a phase diagram (critical depinning field versus disorder strength) qualitatively similar to that obtained numerically on the cubic lattice. We then introduce a specifically tailored random graph that allows an exact asymptotic analysis of the height and width of the interface. We characterize the change of morphology of the interface as a function of the disorder strength, a change that is found to take place at a multicritical point along the depinning-transition line.

cond-mat.stat-mech↗

arXiv2013

Critical scaling in random-field systems: 2 or 3 independent exponents?

We show that the critical scaling behavior of random-field systems with short-range interactions and disorder correlations cannot be described in general by only two independent exponents, contrary to previous claims. This conclusion is based on a theoretical description of the whole (d,N) domain of the d-dimensional random-field O(N) model and points to the role of rare events that are overlooked by the proposed derivations of two-exponent scaling. Quite strikingly, however, the numerical estimates of the critical exponents of the random field Ising model are extremely close to the predictions of the two-exponent scaling, so that the issue cannot be decided on the basis of numerical simulations.

cond-mat.dis-nn↗

arXiv2013

Decorrelation of the static and dynamic length scales in hard-sphere glass-formers

We show that in the equilibrium phase of glass-forming hard-sphere fluids in three dimensions, the static length scales tentatively associated with the dynamical slowdown and the dynamical length characterizing spatial heterogeneities in the dynamics unambiguously decorrelate. The former grow at a much slower rate than the latter when density increases. This observation is valid for the dynamical range that is accessible to computer simulations, which roughly corresponds to that of colloidal experiments. We also find that in this same range, no one-to-one correspondence between relaxation time and point-to-set correlation length exists. These results point to the coexistence of several relaxation mechanisms in the accessible dynamical regime of three-dimensional hard-sphere glass formers.

cond-mat.dis-nn↗

arXiv2013

Dimensional reduction and its breakdown in the 3-dimensional long-range random field Ising model

We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the random-field Ising model in which both the interactions and the correlations of the disorder are long-ranged, i.e. power-law decaying. To some extent the power-law exponents play the role of spatial dimension in a short-range model, which allows us to probe the theoretically predicted existence of a nontrivial critical value separating a region where dimensional reduction holds from one where it is broken, while still considering the physical dimension d=3. By extending our recently developed approach based on a nonperturbative functional renormalization group combined with a supersymmetric formalism, we find that such a critical value indeed exists, provided one chooses a specific relation between the decay exponents of the interactions and of the disorder correlations. This transition from dimensional reduction to its breakdown should therefore be observable in simulations and numerical analyses, if not experimentally.

cond-mat.dis-nn↗

arXiv2013

Effect of pressure on the number of dynamically correlated molecules when approaching the glass transition

We characterize the heterogeneous character of the dynamics of liquids approaching the glass transition through an experimental determination of the number of dynamically correlated molecules N_{corr} as obtained from dynamical susceptibilities. To do so, we have obtained a new set of dielectric spectroscopy data for liquid dibutyl-phtalate on a fine and extended temperature and pressure grid, and we have used it in conjunction with high-pressure data from the literature. We have been able to evaluate the contributions to N_{corr} that are due to fluctuations associated with density and with temperature separately, thereby improving the estimate of N_{corr}. We find that N_{corr} increases along the glass transition line, and more generally along any isochronic line, as pressure increases (up to 1 GPa), a result which is at odds with recent reports and theoretical predictions.

cond-mat.soft↗

arXiv2013

Geometrical Frustration and Static Correlations in Hard-Sphere Glass Formers

We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly irrelevant with increasing dimension. We also find the growth in structural correlations to be modest in the dynamical regime accessible to computer simulations.

cond-mat.stat-mech↗

arXiv2012

Avalanches and dimensional reduction breakdown in the critical behavior of disordered systems

We investigate the connection between a formal property of the critical behavior of several systems in the presence of quenched disorder, known as "dimensional reduction", and the presence in the same systems at zero temperature of collective events known as "avalanches". Avalanches generically produce nonanalyticities in the functional dependence of the cumulants of the renormalized disorder. We show that this leads to a breakdown of the dimensional reduction predictions if and only if the fractal dimension characterizing the scaling properties of the avalanches is exactly equal to the difference between the dimension of space and the scaling dimension of the primary field, e.g. the magnetization in a random field model. This is proven by combining scaling theory and functional renormalization group. We therefore clarify the puzzle of why dimensional reduction remains valid in random field systems above a nontrivial dimension (but fails below), always applies to the statistics of branched polymer and is always wrong in elastic models of interfaces in a random environment.

cond-mat.dis-nn↗