arXiv subjects

G. Parisi

Publications and source records attributed to G. Parisi.

At least 37 records · Page 2Linked to original sources

arXiv2018

The out-equilibrium 2D Ising spin glass: almost, but not quite, a free-field theory

We consider the spatial correlation function of the two-dimensional Ising spin glass under out-equilibrium conditions. We pay special attention to the scaling limit reached upon approaching zero temperature. The field-theory of a non-interacting field makes a surprisingly good job at describing the spatial shape of the correlation function of the out-equilibrium Edwards-Anderson Ising model in two dimensions.

cond-mat.dis-nn↗

arXiv2018

Aging rate of spin glasses from simulations matches experiments

Experiments on spin glasses can now make precise measurements of the exponent $z(T)$ governing the growth of glassy domains, while our computational capabilities allow us to make quantitative predictions for experimental scales. However, experimental and numerical values for $z(T)$ have differed. We use new simulations on the Janus II computer to resolve this discrepancy, finding a time-dependent $z(T, t_w)$, which leads to the experimental value through mild extrapolations. Furthermore, theoretical insight is gained by studying a crossover between the $T = T_c$ and $T = 0$ fixed points.

cond-mat.dis-nn↗

arXiv2018

Support for the value 5/2 for the spin glass lower critical dimension at zero magnetic field

We study numerically various properties of the free energy barriers in the Edwards-Anderson model of spin glasses in the low-temperature region both in three and four spatial dimensions. In particular, we investigated the dependence of height of free energy barriers on system size and on the distance between the initial and final states (i.e. the overlap distance). A related quantity is the distribution of large local fluctuations of the overlap in large three-dimensional samples at equilibrium. Our results for both quantities (barriers and large deviations) are in agreement with the prediction obtained in the framework of mean field theory. In addition, our result supports $D_{lc}=2.5$ as the lower critical dimension for the model.

cond-mat.dis-nn↗

arXiv2017

Dynamic Variational Study of Chaos: Spin Glasses in Three Dimensions

We have introduced a variational method to improve the computation of integrated correlation times in the Parallel Tempering Dynamics, obtaining a better estimate (a lower bound, at least) of the exponential correlation time. Using this determination of the correlation times, we revisited the problem of the characterization of the chaos in temperature in finite dimensional spin glasses by means of the study of correlations between different chaos indicators computed in the static and the correlation times of the Parallel Tempering dynamics. The sample-distribution of the characteristic time for the Parallel Tempering dynamics turns out to be fat-tailed and it obeys finite-size scaling.

cond-mat.dis-nn↗

arXiv2017

Matching microscopic and macroscopic responses in glasses

We first reproduce on the Janus and Janus II computers a milestone experiment that measures the spin-glass coherence length through the lowering of free-energy barriers induced by the Zeeman effect. Secondly we determine the scaling behavior that allows a quantitative analysis of a new experiment reported in the companion Letter [S. Guchhait and R. Orbach, Phys. Rev. Lett. 118, 157203 (2017)]. The value of the coherence length estimated through the analysis of microscopic correlation functions turns out to be quantitatively consistent with its measurement through macroscopic response functions. Further, non-linear susceptibilities, recently measured in glass-forming liquids, scale as powers of the same microscopic length.

cond-mat.dis-nn↗

arXiv2017

A statics-dynamics equivalence through the fluctuation-dissipation ratio provides a window into the spin-glass phase from nonequilibrium measurements

The unifying feature of glass formers (such as polymers, supercooled liquids, colloids, granulars, spin glasses, superconductors, ...) is a sluggish dynamics at low temperatures. Indeed, their dynamics is so slow that thermal equilibrium is never reached in macroscopic samples: in analogy with living beings, glasses are said to age. Here, we show how to relate experimentally relevant quantities with the experimentally unreachable low-temperature equilibrium phase. We have performed a very accurate computation of the non-equilibrium fluctuation-dissipation ratio for the three-dimensional Edwards-Anderson Ising spin glass, by means of large-scale simulations on the special-purpose computers Janus and Janus II. This ratio (computed for finite times on very large, effectively infinite, systems) is compared with the equilibrium probability distribution of the spin overlap for finite sizes. The resulting quantitative statics-dynamics dictionary, based on observables that can be measured with current experimental methods, could allow the experimental exploration of important features of the spin-glass phase without uncontrollable extrapolations to infinite times or system sizes.

cond-mat.dis-nn↗

arXiv2017

Numerical construction of the Aizenman-Wehr metastate

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a "dispersed" metastate, supported on many thermodynamic states.

cond-mat.dis-nn↗

arXiv2016

Temperature chaos is a non-local effect

Temperature chaos plays a role in important effects, like for example memory and rejuvenation, in spin glasses, colloids, polymers. We numerically investigate temperature chaos in spin glasses, exploiting its recent characterization as a rare-event driven phenomenon. The peculiarities of the transformation from periodic to anti-periodic boundary conditions in spin glasses allow us to conclude that temperature chaos is non-local: no bounded region of the system causes it. We precise the statistical relationship between temperature chaos and the free-energy changes upon varying boundary conditions.

cond-mat.dis-nn↗

arXiv2016

A general theorem on the divergence of vortex beams

The propagation and divergence properties of beams carrying orbital angular momentum (OAM) play a crucial role in many applications. Here we present a general study on the divergence of optical beams with OAM. We show that the mean absolute value of the OAM imposes a lower bound on the value of the beam divergence. We discuss our results for two different definitions of the divergence, the so called rms or encircled-energy. The bound on the rms divergence can be expressed as a generalized uncertainty principle, with applications in long-range communication, microscopy and 2D quantum systems.

quant-ph↗

arXiv2016

Universal critical behavior of the 2d Ising spin glass

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

cond-mat.dis-nn↗

arXiv2015

A large-N approximated field theory for multipartite entanglement

We study the characterization of multipartite entanglement for the random states of an $n$-qbit system. Unable to solve the problem exactly we generalize it, changing complex numbers into real vectors with $N_c$ components (the original problem is recovered for $N_c=2$). Studying the leading diagrams in the large-$N_c$ approximation, we unearth the presence of a phase transition and, in an explicit example, show that the so-called entanglement frustration disappears in the large-$N_c$ limit.

quant-ph↗

arXiv2015

Jamming Criticality Revealed by Removing Localized Buckling Excitations

Recent theoretical advances offer an exact, first-principle theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small inter-particle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the inter-particle gaps is known to be constant in all spatial dimensions $d$ -- including the physically relevant $d=2$ and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

cond-mat.stat-mech↗

arXiv2015

Inherent Structures in m-component Spin Glasses

We observe numerically the properties of the infinite-temperature inherent structures of m-component vector spin glasses in three dimensions. An increase of m implies a decrease of the amount of minima of the free energy, down to the trivial presence of a unique minimum. For little m correlations are small and the dynamics are quickly arrested, while for larger m low-temperature correlations crop up and the convergence is slower, to a limit that appears to be related with the system size.

cond-mat.dis-nn↗

arXiv2015

Explicit generation of the branching tree of states in spin glasses

We present a numerical method to generate explicit realizations of the tree of states in mean-field spin glasses. The resulting study illuminates the physical meaning of the full replica symmetry breaking solution and provides detailed information on the structure of the spin-glass phase. A cavity approach ensures that the method is self-consistent and permits the evaluation of sophisticated observables, such as correlation functions. We include an example application to the study of finite-size effects in single-sample overlap probability distributions, a topic that has attracted considerable interest recently.

cond-mat.dis-nn↗

arXiv2014

Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension

We revisited, by means of numerical simulations, the one dimensional bond diluted Levy Ising spin glasses outside the limit of validity of mean field theories. In these models the probability that two spins at distance $r$ interact (via a disordered interactions, $J_{ij}=\pm 1$) decays as $r^{-ρ}$. We have estimated, using finite size scaling techniques, the infinite volume correlation length and spin glass susceptibility for $ρ=5/3$ and $ρ=9/5$. We have obtained strong evidence for divergences of the previous observables at a non zero critical temperature. We discuss the behavior of the critical exponents, especially when approaching the value $ρ=2$, corresponding to a critical threshold beyond which the model has no phase transition. Finally, we numerically study the model right at the threshold value $ρ=2$.

cond-mat.dis-nn↗

arXiv2014

Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties stressed by Newman and Stein concerning the problem of constructing pure states in spin glass systems. We mainly discuss what happens in finite-dimensional, realistic spin glasses. Together with a detailed review of some of the most important features, facts, data, and phenomena, we present some new theoretical ideas and numerical results. We discuss among others the basic idea of the RSB theory, correlation functions, interfaces, overlaps, pure states, random field, and the dynamical approach. We present new numerical results for the behaviors of coupled replicas and about the numerical verification of sum rules, and we review some of the available numerical results that we consider of larger importance (for example, the determination of the phase transition point, the correlation functions, the window overlaps, and the dynamical behavior of the system).

cond-mat.dis-nn↗

arXiv2014

The three dimensional Ising spin glass in an external magnetic field: the role of the silent majority

We perform equilibrium parallel-tempering simulations of the 3D Ising Edwards-Anderson spin glass in a field. A traditional analysis shows no signs of a phase transition. Yet, we encounter dramatic fluctuations in the behaviour of the model: Averages over all the data only describe the behaviour of a small fraction of it. Therefore we develop a new approach to study the equilibrium behaviour of the system, by classifying the measurements as a function of a conditioning variate. We propose a finite-size scaling analysis based on the probability distribution function of the conditioning variate, which may accelerate the convergence to the thermodynamic limit. In this way, we find a non-trivial spectrum of behaviours, where a part of the measurements behaves as the average, while the majority of them shows signs of scale invariance. As a result, we can estimate the temperature interval where the phase transition in a field ought to lie, if it exists. Although this would-be critical regime is unreachable with present resources, the numerical challenge is finally well posed.

cond-mat.dis-nn↗

arXiv2014

Dynamical transition in the D = 3 Edwards-Anderson spin glass in an external magnetic field

We study the off-equilibrium dynamics of the three-dimensional Ising spin glass in the presence of an external magnetic field. We have performed simulations both at fixed temperature and with an annealing protocol. Thanks to the Janus special-purpose computer, based on FPGAs, we have been able to reach times equivalent to 0.01 seconds in experiments. We have studied the system relaxation both for high and for low temperatures, clearly identifying a dynamical transition point. This dynamical temperature is strictly positive and depends on the external applied magnetic field. We discuss different possibilities for the underlying physics, which include a thermodynamical spin-glass transition, a mode-coupling crossover or an interpretation reminiscent of the random first-order picture of structural glasses.

cond-mat.dis-nn↗