arXiv subjects

Giorgio Parisi

Publications and source records attributed to Giorgio Parisi.

At least 145 records · Page 8Linked to original sources

arXiv2012

Quasi-equilibrium in glassy dynamics: an algebraic view

We study a chain of identical glassy systems in a constrained equilibrium where each bond of the chain is forced to remain at a preassigned distance to the previous one. We apply this description to Mean Field Glassy systems in the limit of long chain where each bond is close to the previous one. We show that in specific conditions this pseudo-dynamic process can formally describe real relaxational dynamics the long time. In particular, in mean field spin glass models we can recover in this way the equations of Langevin dynamics in the long time limit at the dynamical transition temperature and below. We interpret the formal identity as an evidence that in these situations the configuration space is explored in a quasi-equilibrium fashion. Our general formalism, that relates dynamics to equilibrium puts slow dynamics in a new perspective and opens the way to the computation of new dynamical quantities in glassy systems.

cond-mat.stat-mech↗

arXiv2012

Universal microstructure and mechanical stability of jammed packings

Jammed packings' mechanical properties depend sensitively on their detailed local structure. Here we provide a complete characterization of the pair correlation close to contact and of the force distribution of jammed frictionless spheres. In particular we discover a set of new scaling relations that connect the behavior of particles bearing small forces and those bearing no force but that are almost in contact. By performing systematic investigations for spatial dimensions d=3-10, in a wide density range and using different preparation protocols, we show that these scalings are indeed universal. We therefore establish clear milestones for the emergence of a complete microscopic theory of jamming. This description is also crucial for high-precision force experiments in granular systems.

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arXiv2012

Dimensional Study of the Caging Order Parameter at the Glass Transition

The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension, we find the cage to keep a non-trivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is here qualitatively supported and non-mean-field corrections are found to remain small on decreasing dimension, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.

cond-mat.stat-mech↗

arXiv2012

Random Pinning Glass Model

Glass transition where viscosity of liquids increases dramatically upon decrease of temperature without any major change in structural properties, remains one of the most challenging problems in condensed matter physics (Cavagna, 2009; Berthier and Biroli, 2011) in spite of tremendous research efforts in last decades. On the other hand disordered freezing of spins in a magnetic materials with decreasing temperature, the so-called spin glass transition, is relatively better understood (Mezard, Parisi and Virasoro, 1987; Castellani and Cavagna, 2005). Previously found similarity between some spin glass models with the structural glasses (Kirkpatrick and Thirumalai, 1987; Kirkpatrick and Wolynes, 1987; Kirkpatrick and Wolynes, 1987; Franz and Parisi, 1999; Moore and Drossel, 2002) inspired development of theories of structural glasses (Kirkpatrick, Thirumalai and Wolynes, 1989; Barrat, Franz and Parisi, 1997; Mézard and Parisi, 1999; Lubchenko and Wolynes, 2007; Biroli and Bouchaud, 2012) based on the scenario of spin glass transition. This scenario though looks very appealing is still far from being well established. One of the main differences between standard spin systems to molecular systems is the absence of quenched disorder and the presence of translational invariance: it often assumed that this difference is not relevant, but this conjecture is still far from being established. The quantities, which are well defined and characterized for spin models, are not easily calculable for molecular glasses due to the lack of quenched disorder which breaks the translational invariance in the system and the characterization of the similarity between the spin and the structural glass transition remained an elusive subject still now. In this study we introduced a model structural glass with built in quenched disorder which alleviates this main difference between the spin and molecular glasses thereby helping us to compare these two systems: the possibility of producing a good thermalization at rather low temperatures is one of the advantages of this model.

cond-mat.stat-mech↗

arXiv2012

Dynamical critical exponents for the mean-field Potts glass

In this paper we study the critical behaviour of the fully-connected p-colours Potts model at the dynamical transition. In the framework of Mode Coupling Theory (MCT), the time autocorrelation function displays a two step relaxation, with two exponents governing the approach to the plateau and the exit from it. Exploiting a relation between statics and equilibrium dynamics which has been recently introduced, we are able to compute the critical slowing down exponents at the dynamical transition with arbitrary precision and for any value of the number of colours p. When available, we compare our exact results with numerical simulations. In addition, we present a detailed study of the dynamical transition in the large p limit, showing that the system is not equivalent to a random energy model.

cond-mat.dis-nn↗

arXiv2012

Critical slowing down exponents in quenched disordered spin models for structural glasses: Random Orthogonal and related models

An important prediction of Mode-Coupling-Theory (MCT) is the relationship between the power- law decay exponents in the β regime. In the original structural glass context this relationship follows from the MCT equations that are obtained making rather uncontrolled approximations and λ has to be treated like a tunable parameter. It is known that a certain class of mean-field spin-glass models is exactly described by MCT equations. In this context, the physical meaning of the so called parameter exponent λ has recently been unveiled, giving a method to compute it exactly in a static framework. In this paper we exploit this new technique to compute the critical slowing down exponents in a class of mean-field Ising spin-glass models including, as special cases, the Sherrington-Kirkpatrick model, the p-spin model and the Random Orthogonal model.

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arXiv2012

On the two-steps relaxation of mean-field glasses: p-spin model

Critical slowing down dynamics of supercooled glass-forming liquids is usually understood at the mean-field level in the framework of Mode Coupling Theory, providing a two-time relaxation scenario and power-law behaviors of the time correlation function at dynamic criticality. In this work we derive critical slowing down exponents of spin-glass models undergoing discontinuous transitions by computing their Gibbs free energy and connecting the dynamic behavior to static "in-state" properties. Both the spherical and Ising versions are considered and, in the simpler spherical case, a generalization to arbitrary schematic Mode Coupling kernels is presented. Comparison with dynamic results available in literature is performed. Analytical predictions for the Ising case are provided for any $p$.

cond-mat.dis-nn↗

arXiv2011

Replica symmetry breaking in and around six dimensions

Two, replica symmetry breaking specific, quantities of the Ising spin glass --- the breakpoint x1 of the order parameter function and the Almeida-Thouless line --- are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results comfirm that replica symmetry breaking does exist below d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x1 has a nonzero and universal value for d<6 at criticality. Near six dimensions we have x1=3(6-d)+O[(6-d)^2]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.

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arXiv2011

Glass transition and random close packing above three dimensions

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.

cond-mat.dis-nn↗

arXiv2011

Field Theory of Fluctuations in Glasses

We develop a field-theoretical description of dynamical heterogeneities and fluctuations in supercooled liquids close to the (avoided) MCT singularity. Using quasi-equilibrium arguments we eliminate time from the description and we completely characterize fluctuations in the beta regime. We identify different sources of fluctuations and show that the most relevant ones are associated to variations of "self-induced disorder" in the initial condition of the dynamics. It follows that heterogeneites can be describes through a cubic field theory with an effective random field term. The phenomenon of perturbative dimensional reduction ensues, well known in random field problems, which implies an upper critical dimension of the theory equal to 8. We apply our theory to finite size scaling for mean-field systems and we test its prediction against numerical simulations.

cond-mat.stat-mech↗

arXiv2011

A numerical study of the overlap probability distribution and its sample-to-sample fluctuations in a mean-field model

In this paper we study the fluctuations of the probability distributions of the overlap in mean field spin glasses in the presence of a magnetic field on the De Almeida-Thouless line. We find that there is a large tail in the left part of the distribution that is dominated by the contributions of rare samples. Different techniques are used to examine the data and to stress on different aspects of the contribution of rare samples.

cond-mat.dis-nn↗

arXiv2011

Replica Field Theory of the Dynamical Transition in Glassy Systems

The critical behaviour of the dynamical transition of glassy system is controlled by a Replica Symmetric action with n=1 replicas. The most divergent diagrams in the loop expansion correspond at all orders to the solutions of a stochastic equation leading to perturbative dimensional reduction. The theory describe accurately numerical simulations of mean-field models.

cond-mat.stat-mech↗

arXiv2011

On the solution of a `solvable' model of an ideal glass of hard spheres displaying a jamming transition

We discuss the analytical solution through the cavity method of a mean field model that displays at the same time an ideal glass transition and a set of jamming points. We establish the equations describing this system, and we discuss some approximate analytical solutions and a numerical strategy to solve them exactly. We compare these methods and we get insight into the reliability of the theory for the description of finite dimensional hard spheres.

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arXiv2010

Interface Energy in the Edwards-Anderson model

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from -1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulate finite temperature systems and work with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension $D_c=2.5$. The results show a good agreement with the mean field theory predictions.

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arXiv2010

A renormalization group computation of the critical exponents of hierarchical spin glasses

The infrared behaviour of a non-mean field spin-glass system is analysed, and the critical exponent related to the divergence of the correlation length is computed at two loops within the epsilon-expansion technique with two independent methods. Both methods yield the same result confirming that the infrared behaviour of the theory if well-defined and the underlying ideas of the Renormalization Group hold also in such non-mean field disordered model. By pushing such calculation to high orders in epsilon, a consistent and predictive non-mean field theory for such disordered system could be established.

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arXiv2010

Critical behaviour of large scale dynamical heterogeneities in glasses: a complete theory

In this talk I will present a complete theory for the behaviour of large-scale dynamical heterogeneities in glasses. Following the work arXiv:1001.1746 I will show that we can write a (physically motivated) simple stochastic differential equation that is potentially able to explain the behaviour of large scale dynamical heterogeneities in glasses. It turns out that this behaviour is in the same universality class of the dynamics near the endpoint of a metastable phase in a disordered system, as far as reparametrization invariant quantities are concerned. Therefore Large scale dynamical heterogeneities in glasses have many points in contact with the Barkhausen noise. Numerical verifications of this theory have not yet done, but they are quite possible.

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arXiv2010

Mean field theory of hard sphere glasses and jamming

Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important problems in information theory, such as digitalization of signals, error correcting codes, and optimization problems. In three dimensions the densest packing of identical hard spheres has been proven to be the FCC lattice, and it is conjectured that the closest packing is ordered (a regular lattice, e.g, a crystal) in low enough dimension. Still, amorphous packings have attracted a lot of interest, because for polydisperse colloids and granular materials the crystalline state is not obtained in experiments for kinetic reasons. We review here a theory of amorphous packings, and more generally glassy states, of hard spheres that is based on the replica method: this theory gives predictions on the structure and thermodynamics of these states. In dimensions between two and six these predictions can be successfully compared with numerical simulations. We will also discuss the limit of large dimension where an exact solution is possible. Some of the results we present here have been already published, but others are original: in particular we improved the discussion of the large dimension limit and we obtained new results on the correlation function and the contact force distribution in three dimensions. We also try here to clarify the main assumptions that are beyond our theory and in particular the relation between our static computation and the dynamical procedures used to construct amorphous packings.

cond-mat.dis-nn↗

arXiv2010

The Hierarchical Random Energy Model

We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occuring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point.

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