arXiv subjects

Giorgio Parisi

Publications and source records attributed to Giorgio Parisi.

At least 127 records · Page 7Linked to original sources

arXiv2013

The overlap in glassy systems

In this paper I will consider many of the various definitions of the overlap and of its probability distribution that have been introduced in the literature starting from the original papers of Edwards and Anderson; I will present also some of the most recent results on the probability distribution of the local overlap in spin glasses. These quantities are related to the fluctuation dissipation relations both in their local and in their global versions.

cond-mat.dis-nn↗

arXiv2013

Dimensional dependence of the Stokes--Einstein relation and its violation

We generalize to higher spatial dimensions the Stokes--Einstein relation (SER) and the leading correction to diffusivity in periodic systems, and validate them using numerical simulations. Using these results, we investigate the evolution of the SER violation with dimension in simple hard sphere glass formers. The analysis suggests that the SER violation disappears around dimension d=8, above which SER is not violated. The critical exponent associated to the violation appears to evolve linearly in 8-d below d=8, as predicted by Biroli and Bouchaud [J. Phys.: Cond. Mat. 19, 205101 (2007)], but the linear coefficient is not consistent with their prediction. The SER violation evolution with d establishes a new benchmark for theory, and a complete description remains an open problem.

cond-mat.stat-mech↗

arXiv2013

Finite size corrections to disordered systems on Erdös-Rényi random graphs

We study the finite size corrections to the free energy density in disorder spin systems on sparse random graphs, using both replica theory and cavity method. We derive an analytical expressions for the $O(1/N)$ corrections in the replica symmetric phase as a linear combination of the free energies of open and closed chains. We perform a numerical check of the formulae on the Random Field Ising Model at zero temperature, by computing finite size corrections to the ground state energy density.

cond-mat.dis-nn↗

arXiv2013

Critical Exponents of the Random Field Hierarchical Model

We have studied the one dimensional Dyson hierarchical model in presence of a random field. This is a long range model where the interactions scale with the distance with a power law-like form J(r) ~ r^{-ρ} and we can explore mean field and non-mean field behavior by changing ρ. Thus, it can be used to approach the phase transitions in finite-dimensional disordered models. We studied the model at T=0 and we numerically computed its critical exponents in the non-mean field region for Gaussian disorder. We then computed an analytic expression for the critical exponent δ, that holds in the non-mean field region, and we noted an interesting relation between the critical exponents of the disordered model and the ones of the pure model, that seems to break down in the non-mean field region. We finally compare our results for the critical exponents with the expected ones in D-dimensional short range models and with the ones of the straightforward one dimensional long range model.

cond-mat.dis-nn↗

arXiv2013

Quantitative field theory of the glass transition

We develop a full microscopic replica field theory of the dynamical transition in glasses. By studying the soft modes that appear at the dynamical temperature we obtain an effective theory for the critical fluctuations. This analysis leads to several results: we give expressions for the mean field critical exponents, and we study analytically the critical behavior of a set of four-points correlation functions from which we can extract the dynamical correlation length. Finally, we can obtain a Ginzburg criterion that states the range of validity of our analysis. We compute all these quantities within the Hypernetted Chain Approximation (HNC) for the Gibbs free energy and we find results that are consistent with numerical simulations.

cond-mat.dis-nn↗

arXiv2013

Ensemble renormalization group for disordered systems

We propose and study a renormalization group transformation that can be used also for models with strong quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g., the ratio of correlations averaged over the ensemble) invariant under the transformation. We validate this ensemble renormalization group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.

cond-mat.dis-nn↗

arXiv2013

Exact theory of dense amorphous hard spheres in high dimension. II. The high density regime and the Gardner transition

We consider the theory of the glass phase and jamming of hard spheres in the large space dimension limit. Building upon the exact expression for the free-energy functional obtained previously, we find that the Random First Order Transition (RFOT) scenario is realized here with two thermodynamic transitions: the usual Kauzmann point associated with entropy crisis, and a further transition at higher pressures in which a glassy structure of micro-states is developed within each amorphous state. This kind of glass-glass transition into a phase dominating the higher densities was described years ago by Elisabeth Gardner, and may well be a generic feature of RFOT. Micro states that are small excitations of an amorphous matrix -- separated by low entropic or energetic barriers -- thus emerge naturally, and modify the high pressure (or low temperature) limit of the thermodynamic functions.

cond-mat.stat-mech↗

arXiv2013

Jamming transition of randomly pinned systems

We consider a system of hard spheres close to jamming, where translation invariance is broken by pinning a randomly chosen set of particles. Using two different protocols, we generate two kinds of packings at the jamming point, isostatic and hyperstatic packings. In the case where the packings are isostatic, jamming transition is not affected by random pinning: the jamming density is only slightly reduced, a generalized isostaticity condition holds, the system is marginally rigid over the entire glass phase, and the typical structural signatures of jamming are unchanged. Besides, random pinning does not have effect on the vibrational modes of the amorphous system, at least on the time and length scale that we are able to probe. For packings that are hyperstatic at jamming, the microscopic properties of the system are strongly affected by the random pinning: the frozen degrees of freedom introduce an excess of constraints that drives the system far from the mechanical marginality conditions and stabilize the low frequency modes of the system, shifting them to higher frequencies. The distance from the isostatic point seems to be the only relevant parameter in the system in both cases. These two cases are in contrast with the behavior of the plane waves of a crystal: the whole spectrum in this case is shifted to higher frequencies as soon as some particles are pinned.

cond-mat.dis-nn↗

arXiv2013

Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field

The Ising model in a random field and with power-law decaying ferromagnetic bonds is studied at zero temperature. Comparing the scaling of the energy contributions of the ferromagnetic domain wall flip and of the random field a la Imry-Ma we obtain a threshold value for the power $ρ$ of the long-range interaction, beyond which no critical behavior occurs. The critical threshold value is $ρ_c=3/2$, at a difference with the zero field model in which $ρ_c=2$. This prediction is confirmed by numerical computation of the ground states below, at, and above this threshold value. Some possible implications for the critical behavior of spin-glasses in a field are conjectured.

cond-mat.dis-nn↗

arXiv2013

Critical Off-Equilibrium Dynamics in Glassy Systems

We consider off-equilibrium dynamics at the critical temperature in a class of glassy system. The off-equilibrium correlation and response functions obey a precise scaling form in the aging regime. The structure of the {\it equilibrium} replicated Gibbs free energy fixes the corresponding {\it off-equilibrium} scaling functions implicitly through two functional equations. The details of the model enter these equations only through the ratio $w_2/w_1$ of the cubic coefficients (proper vertexes) of the replicated Gibbs free energy. Therefore the off-equilibrium dynamical exponents are controlled by the very same parameter exponent $λ=w_2/w_1$ that determines equilibrium dynamics. We find approximate solutions to the equations and validate the theory by means of analytical computations and numerical simulations.

cond-mat.dis-nn↗

arXiv2013

Entropy-Driven Phase Transitions of Entanglement

We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.

quant-ph↗

arXiv2013

Multi-surface coding simulations of the restricted solid-on-solid model in four dimensions

We study the Restricted Solid on Solid (RSOS) model for surface growth in spatial dimension d=4 by means of a multi-surface coding technique that allows to analyze samples to analyze samples of size up to $256^4$ in the steady state regime. For such large systems we are able to achieve a controlled asymptotic regime where the typical scale of the fluctuations are larger than the lattice spacing used in the simulations. A careful finite-size scaling analysis of the critical exponents clearly indicate that d=4 is not the upper critical dimension of the model.

cond-mat.dis-nn↗

arXiv2013

Static replica approach to critical correlations in glassy systems

We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.

cond-mat.stat-mech↗

arXiv2012

Glassy Critical Points and Random Field Ising Model

We consider the critical properties of points of continuous glass transition as one can find in liquids in presence of constraints or in liquids in porous media. Through a one loop analysis we show that the critical Replica Field Theory describing these points can be mapped in the $ϕ^4$-Random Field Ising Model. We confirm our analysis studying the finite size scaling of the $p$-spin model defined on sparse random graph, where a fraction of variables is frozen such that the phase transition is of a continuous kind.

cond-mat.stat-mech↗

arXiv2012

Critical Dynamics in Glassy Systems

Critical dynamics in various glass models including those described by mode coupling theory is described by scale-invariant dynamical equations with a single non-universal quantity, i.e. the so-called parameter exponent that determines all the dynamical critical exponents. We show that these equations follow from the structure of the static replicated Gibbs free energy near the critical point. In particular the exponent parameter is given by the ratio between two cubic proper vertexes that can be expressed as six-point cumulants measured in a purely static framework.

cond-mat.dis-nn↗

arXiv2012

A note on weakly discontinuous dynamical transitions

We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "$A_3$" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from the details of the system. The analysis of this limiting case suggests new ways for looking at the Mode Coupling equations in the general case.

cond-mat.stat-mech↗

arXiv2012

Exact theory of dense amorphous hard spheres in high dimension. I. The free energy

We consider the theory of the glass transition and jamming of hard spheres in the large space dimension limit. Previous investigations were based on the assumption that the probability distribution within a "cage" is Gaussian, which is not fully consistent with numerical results. Here we perform a replica calculation without making any assumption on the cage shape. We show that thermodynamic functions turn out to be exact within the Gaussian ansatz -- provided one allows for arbitrary replica symmetry breaking --- and indeed agree well with numerical results. The actual structure function (the so-called non-ergodic parameter) is not Gaussian, an apparent paradox which we discuss. In this paper we focus on the free energy, future papers will present the results for the structure functions and a detailed comparison with numerical results.

cond-mat.stat-mech↗

arXiv2012

Generalized Fluctuation-Dissipation Relation and Effective Temperature upon Heating a Deeply Supercooled Liquid

We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time-dependence and that it retains its connection with the partitioned phase space visited in ageing. We underline the potential relevance of our numerical results for experimental studies of the fluctuation-dissipation relation in glassy systems.

cond-mat.stat-mech↗