Publications (138)429.66 Total impact
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ABSTRACT: In the threedimensional Heisenberg spin glass in a random field we study the properties of the inherent structures that are obtained by an instantaneous cooling from infinite temperature. For not too large field the density of states $g(\omega)$ develops localized soft {\em plastic} modes and reaches zero as $\omega^4$ (for large fiels a gap appears). When we perturb the system adding a force along the softest mode one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical twolevel systems.  [Show abstract] [Hide abstract]
ABSTRACT: We study the threedimensional Heisenberg spin glass in a random field. For large fields a gap appears, while when they are small the density of states $g(\omega)$ develops localized soft modes and reaches zero as $\omega^4$. By imposing a force along the softest mode one reaches very similar minima of the energy, separated by small barriers, that appear to be good candidates for classical twolevel systems.  [Show abstract] [Hide abstract]
ABSTRACT: The staticsdynamics correspondence in spin glasses relate nonequilibrium results on large samples (the experimental realm) with equilibrium quantities computed on small systems (the typical arena for theoretical computations). Here we employ staticsdynamics equivalence to study the Ising spinglass critical behavior in three dimensions. By means of Monte Carlo simulation, we follow the growth of the coherence length (the size of the glassy domains), on lattices too large to be thermalized. Thanks to the large coherence lengths we reach, we are able to obtain accurate results in excellent agreement with the best available equilibrium computations. To do so, we need to clarify the several physical meanings of the dynamic exponent close to the critical temperature.  [Show abstract] [Hide abstract]
ABSTRACT: We study the critical behavior of the threedimensional Ising spin glass under experimentally relevant conditions: very large systems that never reach equilibrium. We compute a coherence length that measures the size of the growing magnetic glassy domains. At the critical point, we reach coherencelengths larger than in any previous numerical study thanks to our optimized Monte Carlo method. The timedependent coherent length allows us to conduct an accurate finitesize scaling (dubbed finitetime scaling) study of the spinglass transition. We find sizeable corrections to scaling, that we control. We suggest that the very same scaling corrections are the underlying reason for Universality issues previously found in experimental studies of spinglasses.  [Show abstract] [Hide abstract]
ABSTRACT: We use a sampledependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution of the SherringtonKirkpatrick and $3D$ EdwardsAnderson models of Ising spin glasses. We find that this approach is an effective tool to distinguish between replica symmetry breaking\char21{}like and dropletlike behavior of the spinglass phase. Our results are in agreement with a replica symmetry breaking\char21{}like behavior for the $3D$ EdwardsAnderson model.  [Show abstract] [Hide abstract]
ABSTRACT: We perform equilibrium paralleltempering simulations of the 3D Ising EdwardsAnderson 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 finitesize 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 nontrivial 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 wouldbe critical regime is unreachable with present resources, the numerical challenge is finally well posed.  [Show abstract] [Hide abstract]
ABSTRACT: We study the offequilibrium dynamics of the threedimensional 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 specialpurpose computer, based on fieldprogrammable gate array (FPGAs), we have been able to reach times equivalent to 0.01 s 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 spinglass transition, a modecoupling crossover, or an interpretation reminiscent of the random firstorder picture of structural glasses.  [Show abstract] [Hide abstract]
ABSTRACT: We report a highprecision finitesize scaling study of the critical behavior of the threedimensional Ising EdwardsAnderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leadingorder corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, \nu = 2.562(42) for the thermal exponent, \eta = 0.3900(36) for the anomalous dimension and \omega = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield \alpha = 5.69(13), \beta = 0.782(10) and \gamma = 6.13(11). We also compute several universal quantities at Tc.  [Show abstract] [Hide abstract]
ABSTRACT: This paper describes the architecture, the development and the implementation of Janus II, a new generation applicationdriven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of highperformance computing: the resources necessary to study in detail theoretical models that can make contact with experimental data are by far beyond those available using commodity computer systems. On the other hand, several specific features of the associated algorithms suggest that unconventional computer architectures, which can be implemented with available electronics technologies, may lead to order of magnitude increases in performance, reducing to acceptable values on human scales the time needed to carry out simulation campaigns that would take centuries on commercially available machines. Janus II is one such machine, recently developed and commissioned, that builds upon and improves on the successful JANUS machine, which has been used for physics since 2008 and is still in operation today. This paper describes in detail the motivations behind the project, the computational requirements, the architecture and the implementation of this new machine and compares its expected performances with those of currently available commercial systems.  [Show abstract] [Hide abstract]
ABSTRACT: We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark the presence of strong finitesize effects on the chiral sector. We find a unique phase transition for the chiral and spin glass sector, in the Universality class of Ising spin glasses. We focus on keeping finitesize effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 64x64x64 spins, over a vast range of temperatures.  [Show abstract] [Hide abstract]
ABSTRACT: Temperature chaos has often been reported in literature as a rareevent driven phenomenon. However, this fact has always been ignored in the data analysis, thus erasing the signal of the chaotic behavior (still rare in the sizes achieved) and leading to an overall picture of a weak and gradual phenomenon. On the contrary, our analysis relies on a largedeviations functional that allows to discuss the size dependencies. In addition, we had at our disposal unprecedentedly large configurations equilibrated at low temperatures, thanks to the Janus computer. According to our results, when temperature chaos occurs its effects are strong and can be felt even at short distances. 
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ABSTRACT: We solve a longstanding puzzle in statistical mechanics of disordered systems. By performing a highstatistics simulation of the D=3 randomfield Ising model at zero temperature for different shapes of the randomfield distribution, we show that the model is ruled by a single universality class. We compute the complete set of critical exponents for this class, including the correctiontoscaling exponent, and we show, to high numerical accuracy, that scaling is described by two independent exponents. Discrepancies with previous works are explained in terms of strong scaling corrections.  [Show abstract] [Hide abstract]
ABSTRACT: A Comment on the Letter by B. Yucesoy, H. G. Katzgraber, and J. Machta, Phys. Rev. Lett. 109, 177204 (2012). The authors of the Letter offer a Reply.  [Show abstract] [Hide abstract]
ABSTRACT: In this chapter we describe the Janus supercomputer, a massively parallel FPGAbased system optimized for the simulation of spinglasses, theoretical models that describe the behavior of glassy materials. The custom architecture of Janus has been developed to meet the computational requirements of these models. Spinglass simulations are performed using Monte Carlo methods that lead to algorithms characterized by (1) intrinsic parallelism allowing us to implement many Monte Carlo update engines within a single FPGA; (2) rather small data base (2 MByte) that can be stored onchip, significantly boosting bandwidth and reducing latency. (3) need to generate a large number of goodquality long (≥ 32 bit) random numbers; (4) mostly integer arithmetic and bitwise logic operations. Careful tailoring of the architecture to the specific features of these algorithms has allowed us to embed up to 1024 special purpose cores within just one FPGA, so that simulations of systems that would take centuries on conventional architectures can be performed in just a few months.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we present a general description of the ISDEP code (Integrator of Stochastic Differential Equations for Plasmas) and a brief overview of its physical results and applications so far. ISDEP is a Monte Carlo code that calculates the distribution function of a minority population of ions in a magnetized plasma. It solves the ion equations of motion taking into account the complex 3D structure of fusion devices, the confining electromagnetic field and collisions with other plasma species. The Monte Carlo method used is based on the equivalence between the Fokker–Planck and Langevin equations. This allows ISDEP to run in distributed computing platforms without communication between nodes with almost linear scaling. This paper intends to be a general description and a reference paper in ISDEP. 
Conference Paper: Spin glass simulations on the janus architecture: a desperate quest for strong scaling
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ABSTRACT: We describe Janus, an applicationdriven architecture for Monte Carlo simulations of spin glasses. Janus is a massively parallel architecture, based on reconfigurable FPGA nodes; it offers two orders of magnitude better performance than commodity systems for spin glass applications. The first generation Janus machine has been operational since early 2008; we are currently developing a new generation, that will be on line in early 2013. In this paper we present the Janus architecture, describe both implementations and compare their performances with those of commodity systems.  [Show abstract] [Hide abstract]
ABSTRACT: We compare the critical behavior of the shortrange Ising spin glass with a spin glass with longrange interactions which fall off as a power sigma of the distance. We show that there is a value of sigma of the longrange model for which the critical behavior is very similar to that of the shortrange model in four dimensions. We also study a value of sigma for which we find the critical behavior to be compatible with that of the three dimensional model, though we have much less precision than in the fourdimensional case.  [Show abstract] [Hide abstract]
ABSTRACT: The low temperature excitations in the anisotropic antiferromagnetic ${\mathrm{Fe}}_{1$${}\mathrm{x}}{\mathrm{Zn}}_{\mathrm{x}}{\mathrm{F}}_{2}$ for $x=0.25$ and $0.31$, at and just above the magnetic percolation threshold concentration ${x}_{\mathrm{p}}=0.25$, were measured using inelastic neutron scattering. The excitations were simulated for $x=0.31$ using a localized, classical excitation model, which accounts well for the energies and relative intensities of the excitations observed in the scattering experiments. 
Conference Paper: Janus2: an FPGAbased supercomputer for spin glass simulations
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ABSTRACT: We describe the past and future of the Janus project. The collaboration started in 2006 and deployed in early 2008 the Janus supercomputer, a facility that allowed to speedup Monte Carlo Simulations of a class of model glassy systems and provided unprecedented results for some paradigms in Statistical Mechanics. The Janus Supercomputer was based on stateoftheart FPGA technology, and provided almost two order of magnitude improvement in terms of cost/performance and power/performance ratios. More than four years later, commercial facilities are closingup in terms of performance, but FPGA technology has largely improved. A new generation supercomputer, Janus2, will be able to improve by more than one orders of magnitude with respect to the previous one, and will accordingly be again the best choice in Monte Carlo simulations of Spin Glasses for several years to come with respect to commercial solutions.
Publication Stats
3k  Citations  
429.66  Total Impact Points  
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Institutions

19952014

Complutense University of Madrid
 • Department of Theoretical physics I
 • Facultad de Ciencias Físicas
Madrid, Madrid, Spain


2006

Institute for Biocomputation and Physics of Complex Systems
Caesaraugusta, Aragon, Spain


19992002

Università degli Studi di Roma "La Sapienza"
 Department of Physics
Roma, Latium, Italy
