arXiv subjects

G. Parisi

Publications and source records attributed to G. Parisi.

At least 73 records · Page 4Linked to original sources

arXiv2010

Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition

A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Using different finite size scaling methods evidence for a spin-glass transition is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new method is discussed, that can be exported to systems in a magnetic field.

physics.comp-ph↗

arXiv2010

The Heisenberg spin glass model on GPU: myths and actual facts

We describe different implementations of the 3D Heisenberg spin glass model for Graphics Processing Units (GPU). The results show that the {\em fast} shared memory gives better performance with respect to the {\em slow} global memory only if a multi-hit technique is used.

cond-mat.dis-nn↗

arXiv2010

Nature of the spin-glass phase at experimental length scales

We present a massive equilibrium simulation of the three-dimensional Ising spin glass at low temperatures. The Janus special-purpose computer has allowed us to equilibrate, using parallel tempering, L=32 lattices down to T=0.64 Tc. We demonstrate the relevance of equilibrium finite-size simulations to understand experimental non-equilibrium spin glasses in the thermodynamical limit by establishing a time-length dictionary. We conclude that non-equilibrium experiments performed on a time scale of one hour can be matched with equilibrium results on L=110 lattices. A detailed investigation of the probability distribution functions of the spin and link overlap, as well as of their correlation functions, shows that Replica Symmetry Breaking is the appropriate theoretical framework for the physically relevant length scales. Besides, we improve over existing methodologies to ensure equilibration in parallel tempering simulations.

cond-mat.dis-nn↗

arXiv2010

A note on rattlers in amorphous packings of binary mixtures of hard spheres

It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our theoretical result for the jamming density of a binary mixture of hard spheres (arXiv:0903.5099) apparently violates an upper bound that is obtained by considering the limit where the diameter ratio r = DA/DB goes to infinity. We believe that this apparent contradiction is the consequence of a misunderstanding, which we try to clarify here.

cond-mat.soft↗

arXiv2010

Critical Behavior of Three-Dimensional Disordered Potts Models with Many States

We study the 3D Disordered Potts Model with p=5 and p=6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower $p$ values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime.

cond-mat.dis-nn↗

arXiv2010

A phase-separation perspective on dynamic heterogeneities in glass-forming liquids

We study dynamic heterogeneities in a model glass-former whose overlap with a reference configuration is constrained to a fixed value. The system phase-separates into regions of small and large overlap, so that dynamical correlations remain strong even for asymptotic times. We calculate an appropriate thermodynamic potential and find evidence of a Maxwell's construction consistent with a spinodal decomposition of two phases. Our results suggest that dynamic heterogeneities are the expression of an ephemeral phase-separating regime ruled by a finite surface tension.

cond-mat.dis-nn↗

arXiv2010

Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated to very entangled states, and one at a negative temperature, signalling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to 2-D quantum gravity) and study the finite size corrections to the saddle point solution.

quant-ph↗

arXiv2009

Spin Glasses on the Hypercube

We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are: (i) the dynamics is ruled by an infinite number of time-sectors, (ii) the aging dynamics consists on the growth of coherent domains with a non vanishing surface-volume ratio, and (iii) the propagator in Fourier space follows the p^4 law. We study as well finite D effects in the nonequilibrium dynamics, finding that a naive finite size scaling ansatz works surprisingly well.

cond-mat.dis-nn↗

arXiv2009

Multipartite Entanglement and Frustration

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration arises. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.

quant-ph↗

arXiv2009

Ising spin glass transition in magnetic field out of mean-field

The spin-glass transition in external magnetic field is studied both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Evidence for a spin-glass transition in magnetic field is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field.

cond-mat.dis-nn↗

arXiv2008

The Spin Glass Phase in the Four-State, Three-Dimensional Potts Model

We perform numerical simulations, including parallel tempering, on the Potts glass model with binary random quenched couplings using the JANUS application-oriented computer. We find and characterize a glassy transition, estimating the location of the transition and the value of the critical exponents. We show that there is no ferromagnetic transition in a large temperature range around the glassy critical temperature. We also compare our results with those obtained recently on the "random permutation" Potts glass.

cond-mat.dis-nn↗

arXiv2008

An in-depth view of the microscopic dynamics of Ising spin glasses at fixed temperature

Using the dedicated computer Janus, we follow the nonequilibrium dynamics of the Ising spin glass in three dimensions for eleven orders of magnitude. The use of integral estimators for the coherence and correlation lengths allows us to study dynamic heterogeneities and the presence of a replicon mode and to obtain safe bounds on the Edwards-Anderson order parameter below the critical temperature. We obtain good agreement with experimental determinations of the temperature-dependent decay exponents for the thermoremanent magnetization. This magnitude is observed to scale with the much harder to measure coherence length, a potentially useful result for experimentalists. The exponents for energy relaxation display a linear dependence on temperature and reasonable extrapolations to the critical point. We conclude examining the time growth of the coherence length, with a comparison of critical and activated dynamics.

cond-mat.dis-nn↗

arXiv2008

Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds

We study numerically the nonequilibrium dynamics of the Ising Spin Glass, for a time that spans eleven orders of magnitude, thus approaching the experimentally relevant scale (i.e. {\em seconds}). We introduce novel analysis techniques that allow to compute the coherence length in a model-independent way. Besides, we present strong evidence for a replicon correlator and for overlap equivalence. The emerging picture is compatible with non-coarsening behavior.

cond-mat.dis-nn↗

arXiv2008

JANUS: an FPGA-based System for High Performance Scientific Computing

This paper describes JANUS, a modular massively parallel and reconfigurable FPGA-based computing system. Each JANUS module has a computational core and a host. The computational core is a 4x4 array of FPGA-based processing elements with nearest-neighbor data links. Processors are also directly connected to an I/O node attached to the JANUS host, a conventional PC. JANUS is tailored for, but not limited to, the requirements of a class of hard scientific applications characterized by regular code structure, unconventional data manipulation instructions and not too large data-base size. We discuss the architecture of this configurable machine, and focus on its use on Monte Carlo simulations of statistical mechanics. On this class of application JANUS achieves impressive performances: in some cases one JANUS processing element outperfoms high-end PCs by a factor ~ 1000. We also discuss the role of JANUS on other classes of scientific applications.

cs.AR↗

arXiv2008

Phase transitions of bipartite entanglement

We study a random matrix model for the statistical properties of the purity of a bipartite quantum system at a finite (fictitious) temperature. This enables us to write the generating function for the cumulants, for both balanced and unbalanced bipartitions. It also unveils an unexpected feature of the system, namely the existence of two phase transitions, characterized by different spectra of the density matrices. One of the critical phases is described by the statistical mechanics of random surfaces, the other is a second-order phase transition.

quant-ph↗

arXiv2008

Diluted one-dimensional spin glasses with power law decaying interactions

We introduce a diluted version of the one dimensional spin-glass model with interactions decaying in probability as an inverse power of the distance. In this model varying the power corresponds to change the dimension in short-range models. The spin-glass phase is studied in and out of the range of validity of the mean-field approximation in order to discriminate between different theories. Since each variable interacts only with a finite number of others the cost for simulating the model is drastically reduced with respect to the fully connected version and larger sizes can be studied. We find both static and dynamic evidence in favor of the so-called replica symmetry breaking theory.

cond-mat.dis-nn↗

arXiv2007

Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study

Numerical models indicate that collective animal behaviour may emerge from simple local rules of interaction among the individuals. However, very little is known about the nature of such interaction, so that models and theories mostly rely on aprioristic assumptions. By reconstructing the three-dimensional position of individual birds in airborne flocks of few thousands members, we prove that the interaction does not depend on the metric distance, as most current models and theories assume, but rather on the topological distance. In fact, we discover that each bird interacts on average with a fixed number of neighbours (six-seven), rather than with all neighbours within a fixed metric distance. We argue that a topological interaction is indispensable to maintain flock's cohesion against the large density changes caused by external perturbations, typically predation. We support this hypothesis by numerical simulations, showing that a topological interaction grants significantly higher cohesion of the aggregation compared to a standard metric one.

q-bio.PE↗

arXiv2007

Ultrametricity in the Edwards-Anderson Model

We test the property of ultrametricity for the spin glass three-dimensional Edwards-Anderson model in zero magnetic field with numerical simulations up to $20^3$ spins. We find an excellent agreement with the prediction of the mean field theory. Since ultrametricity is not compatible with a trivial structure of the overlap distribution our result contradicts the droplet theory.

cond-mat.dis-nn↗