arXiv subjects

M. Tarzia

Publications and source records attributed to M. Tarzia.

18 recordsLinked to original sources

arXiv2018

Random-Field Ising like effective theory of the glass transition: I Mean-Field Models

In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field with an equilibrium reference configuration---close to the putative thermodynamic glass transition. Our starting point is the mean-field theory of glass formation which relies on the existence of a complex free-energy landscape with a multitude of metastable states. In this paper, we focus on archetypal mean-field models possessing this type of free-energy landscape and set up the framework to determine the exact effective theory. We show that the effective theory at the mean-field level is generically of the random-field + random-bond Ising type. We also discuss what are the main issues concerning the extension of our result to finite-dimensional systems. This extension is addressed in detail in the companion paper.

cond-mat.stat-mech↗

arXiv2018

Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the case of finite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.

cond-mat.stat-mech↗

arXiv2012

Difference between level statistics, ergodicity and localization transitions on the Bethe lattice

We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase is a very heterogenous transport that proceeds over a few disorder dependent paths only. We show that the transition to the usual ergodic delocalized phase, which takes place for a disorder strength smaller than the one leading to the localization transition, is related to the freezing-glass transition of directed polymers in random media. The numerical study of level and eigenstate statistics, and of the singular properties of the probability distribution of the local density of states all support the existence of this new intermediate phase. Our results suggest that the localization transition may change nature in high dimensional systems.

cond-mat.dis-nn↗

arXiv2012

On the fragility of the mean-field scenario of structural glasses for finite-dimensional disordered spin models

At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of "structural glasses", with a "random first-order transition" (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated e.g. with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension whereas, despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full-blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.

cond-mat.dis-nn↗

arXiv2008

The Valence Bond Glass phase

We show that a new glassy phase can emerge in presence of strong magnetic frustration and quantum fluctuations. It is a Valence Bond Glass. We study its properties solving the Hubbard-Heisenberg model on a Bethe lattice within the large $N$ limit introduced by Affleck and Marston. We work out the phase diagram that contains Fermi liquid, dimer and valence bond glass phases. This new glassy phase has no electronic or spin gap (although a pseudo-gap is observed), it is characterized by long-range critical valence bond correlations and is not related to any magnetic ordering. As a consequence it is quite different from both valence bond crystals and spin glasses.

cond-mat.str-el↗

arXiv2007

Group testing with Random Pools: Phase Transitions and Optimal Strategy

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible queries, a problem which has relevant practical applications in different fields including molecular biology and computer science. Here we study GT in the probabilistic setting focusing on the regime of small defective probability and large number of objects, $p \to 0$ and $N \to \infty$. We construct and analyze one-stage algorithms for which we establish the occurrence of a non-detection/detection phase transition resulting in a sharp threshold, $\bar M$, for the number of tests. By optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling $\bar M\propto Np|\log p|$. Then we consider two-stages algorithms and analyze their performance for different choices of the first stage pools. In particular, via a proper random choice of the pools, we construct algorithms which attain the optimal value (previously determined in Ref. [16]) for the mean number of tests required for complete detection. We finally discuss the optimal pool design in the case of finite $p$.

cond-mat.stat-mech↗

arXiv2007

Statistical Mechanics of the Hyper Vertex Cover Problem

We introduce and study a new optimization problem called Hyper Vertex Cover. This problem is a generalization of the standard vertex cover to hypergraphs: one seeks a configuration of particles with minimal density such that every hyperedge of the hypergraph contains at least one particle. It can also be used in important practical tasks, such as the Group Testing procedures where one wants to detect defective items in a large group by pool testing. Using a Statistical Mechanics approach based on the cavity method, we study the phase diagram of the HVC problem, in the case of random regualr hypergraphs. Depending on the values of the variables and tests degrees different situations can occur: The HVC problem can be either in a replica symmetric phase, or in a one-step replica symmetry breaking one. In these two cases, we give explicit results on the minimal density of particles, and the structure of the phase space. These problems are thus in some sense simpler than the original vertex cover problem, where the need for a full replica symmetry breaking has prevented the derivation of exact results so far. Finally, we show that decimation procedures based on the belief propagation and the survey propagation algorithms provide very efficient strategies to solve large individual instances of the hyper vertex cover problem.

cond-mat.stat-mech↗

arXiv2007

Glass Phenomenology from the Connection to Spin Glasses

Typical features of glass phenomenology such as the Vogel-Fulcher law, the Kauzmann paradox and the Adam-Gibbs relationship are shown to follow from the recently discovered mapping of glasses to Ising spin glasses in a magnetic field. There seems to be sufficient universality near the glass transition temperature $T_g$ such that study of the spin glass system can provide semi-quantitative results for supercooled liquids.

cond-mat.dis-nn↗

arXiv2007

On the absence of the glass transition in two dimensional hard disks

In this paper we study the glass transition in a model of identical hard spheres, focusing on the two dimensional case. In the mean-field limit the model exhibits an ideal glass transition of the same nature of that found in discontinuous spin glasses. Nevertheless, a systematic expansion around the mean-field solution seems to indicate that the glass transitions is smeared out in two dimensions, in agreement with some recent results. Our investigation could be generalized to higher spatial dimensions, providing a way to determine the lower critical dimensionality of the mean-field ideal glass picture.

cond-mat.stat-mech↗

arXiv2006

Columnar and lamellar phases in attractive colloidal systems

In colloidal suspensions, the competition between attractive and repulsive interactions gives rise to a rich and complex phenomenology. Here, we study the equilibrium phase diagram of a model system using a DLVO interaction potential by means of molecular dynamics simulations and a thermodynamical approach. As a result, we find tubular and lamellar phases at low volume fraction. Such phases, extremely relevant for designing new materials, may be not easily observed in the experiments because of the long relaxation times and the presence of defects.

cond-mat.soft↗

arXiv2006

Pattern formation and glassy phase in the $ϕ^4$ theory with screened electrostatic repulsion

We study analytically the structural properties of a system with a short-range attraction and a competing long-range screened repulsion. This model contains the essential features of the effective interaction potential among charged colloids in polymeric solutions and provides novel insights on the equilibrium phase diagram of these systems. Within the self-consistent Hartree approximation and by using a replica approach, we show that varying the parameters of the repulsive potential and the temperature yields a phase coexistence, a lamellar and a glassy phase. Our results strongly suggest that the cluster phase observed in charged colloids might be the signature of an underlying equilibrium lamellar phase, hidden on experimental time scales.

cond-mat.soft↗

arXiv2006

Granular segregation under vertical tapping

We present extensive Molecular Dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as, shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both Brazil Nut Effect (larger particles on the top, BN) and the Reverse Brazil Nut Effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive ``segregation diagram'' and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.

cond-mat.soft↗

arXiv2005

Size segregation in granular media induced by phase transition

In order to study analytically the nature of the size segregation in granular mixtures, we introduce a mean field theory in the framework of a statistical mechanics approach, based on Edwards' original ideas. For simplicity we apply the theory to a lattice model for hard sphere binary mixture under gravity, and we find a new purely thermodynamic mechanism which gives rise to the size segregation phenomenon. By varying the number of small grains and the mass ratio, we find a crossover from Brasil nut to reverse Brasil nut effect, which becomes a true phase transition when the number of small grains is larger then a critical value. We suggest that this transition is induced by the effective attraction between large grains due to the presence of small ones (depletion force). Finally the theoretical results are confirmed by numerical simulations of the 3d system under taps.

cond-mat.stat-mech↗

arXiv2004

Jamming transition in granular media: A mean field approximation and numerical simulations

In order to study analytically the nature of the jamming transition in granular material, we have considered a cavity method mean field theory, in the framework of a statistical mechanics approach, based on Edwards' original idea. For simplicity we have applied the theory to a lattice model and a transition with exactly the same nature of the glass transition in mean field models for usual glass formers is found. The model is also simulated in three dimensions under tap dynamics and a jamming transition with glassy features is observed. In particular two step decays appear in the relaxation functions and dynamic heterogeneities resembling ones usually observed in glassy systems. These results confirm early speculations about the connection between the jamming transition in granular media and the glass transition in usual glass formers, giving moreover a precise interpretation of its nature.

cond-mat.stat-mech↗

arXiv2004

Statistical Mechanics of segregation in binary granular mixtures

We discuss mixing/segregation phenomena in a schematic hard spheres lattice model for binary mixtures of granular media, by analytical evaluation, within Bethe-Peierls approximation, of Edwards' partition function. The presence of fluid-crystal phase transitions in the system drives segregation as a form of phase separation. Within a pure phase, gravity can also induce a kind of vertical segregation not associated to phase transitions.

cond-mat.stat-mech↗

arXiv2004

Glass transition in granular media

In the framework of schematic hard spheres lattice models for granular media we investigate the phenomenon of the ``jamming transition''. In particular, using Edwards' approach, by analytical calculations at a mean field level, we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. Interestingly, the nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers.

cond-mat.stat-mech↗

arXiv2004

Statistical Mechanics of jamming and segregation in granular media

In the framework of schematic hard spheres lattice models we discuss Edwards' Statistical Mechanics approach to granular media. As this approach appears to hold here to a very good approximation, by analytical calculations of Edwards' partition function at a mean field level we derive the system phase diagram and show that ``jamming'' corresponds to a phase transition from a ``fluid'' to a ``glassy'' phase, observed when crystallization is avoided. The nature of such a ``glassy'' phase turns out to be the same found in mean field models for glass formers. In the same context, we also briefly discuss mixing/segregation phenomena of binary mixtures: the presence of fluid-crystal phase transitions drives segregation as a form of phase separation and, within a given phase, gravity can also induce a kind of ``vertical'' segregation, usually not associated to phase transitions.

cond-mat.stat-mech↗

arXiv2002

A lattice glass model with no tendency to crystallize

We study a lattice model with two body interactions that reproduces in three-dimensions many features of structural glasses, like cage effect and vanishing diffusivity. While having a crystalline state at low temperatures, it does not crystallize when quenched, even at the slowest cooling rate used, which makes it suitable to study the glass transition. We study the model on the Bethe lattice as well, and find a scenario typical of p-spin models, as in the Biroli Mezard model.

cond-mat.stat-mech↗