arXiv subjects

A. Cruz

Publications and source records attributed to A. Cruz.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2013

Critical parameters of the three-dimensional Ising spin glass

We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, ν= 2.562(42) for the thermal exponent, η= -0.3900(36) for the anomalous dimension and ω= 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield α= -5.69(13), β= 0.782(10) and γ= 6.13(11). We also compute several universal quantities at Tc.

cond-mat.dis-nn↗

arXiv2013

Janus II: a new generation application-driven computer for spin-system simulations

This paper describes the architecture, the development and the implementation of Janus II, a new generation application-driven number cruncher optimized for Monte Carlo simulations of spin systems (mainly spin glasses). This domain of computational physics is a recognized grand challenge of high-performance 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.

cs.AR↗

arXiv2012

Reconfigurable computing for Monte Carlo simulations: results and prospects of the Janus project

We describe Janus, a massively parallel FPGA-based computer optimized for the simulation of spin glasses, theoretical models for the behavior of glassy materials. FPGAs (as compared to GPUs or many-core processors) provide a complementary approach to massively parallel computing. In particular, our model problem is formulated in terms of binary variables, and floating-point operations can be (almost) completely avoided. The FPGA architecture allows us to run many independent threads with almost no latencies in memory access, thus updating up to 1024 spins per cycle. We describe Janus in detail and we summarize the physics results obtained in four years of operation of this machine; we discuss two types of physics applications: long simulations on very large systems (which try to mimic and provide understanding about the experimental non-equilibrium dynamics), and low-temperature equilibrium simulations using an artificial parallel tempering dynamics. The time scale of our non-equilibrium simulations spans eleven orders of magnitude (from picoseconds to a tenth of a second). On the other hand, our equilibrium simulations are unprecedented both because of the low temperatures reached and for the large systems that we have brought to equilibrium. A finite-time scaling ansatz emerges from the detailed comparison of the two sets of simulations. Janus has made it possible to perform spin-glass simulations that would take several decades on more conventional architectures. The paper ends with an assessment of the potential of possible future versions of the Janus architecture, based on state-of-the-art technology.

cond-mat.dis-nn↗

arXiv2012

Thermodynamic glass transition in a spin glass without time-reversal symmetry

Spin glasses are a longstanding model for the sluggish dynamics that appears at the glass transition. However, spin glasses differ from structural glasses for a crucial feature: they enjoy a time reversal symmetry. This symmetry can be broken by applying an external magnetic field, but embarrassingly little is known about the critical behaviour of a spin glass in a field. In this context, the space dimension is crucial. Simulations are easier to interpret in a large number of dimensions, but one must work below the upper critical dimension (i.e., in d<6) in order for results to have relevance for experiments. Here we show conclusive evidence for the presence of a phase transition in a four-dimensional spin glass in a field. Two ingredients were crucial for this achievement: massive numerical simulations were carried out on the Janus special-purpose computer, and a new and powerful finite-size scaling method.

cond-mat.dis-nn↗

arXiv2011

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, Stochastic Stability and Overlap Equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda-Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks

cond-mat.dis-nn↗

arXiv2010

Static versus dynamic heterogeneities in the D = 3 Edwards-Anderson-Ising spin glass

We numerically study the aging properties of the dynamical heterogeneities in the Ising spin glass. We find that a phase transition takes place during the aging process. Statics-dynamics correspondence implies that systems of finite size in equilibrium have static heterogeneities that obey Finite-Size Scaling, thus signaling an analogous phase transition in the thermodynamical limit. We compute the critical exponents and the transition point in the equilibrium setting, and use them to show that aging in dynamic heterogeneities can be described by a Finite-Time Scaling Ansatz, with potential implications for experimental work.

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

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↗

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↗

arXiv2007

Simulating spin systems on IANUS, an FPGA-based computer

We describe the hardwired implementation of algorithms for Monte Carlo simulations of a large class of spin models. We have implemented these algorithms as VHDL codes and we have mapped them onto a dedicated processor based on a large FPGA device. The measured performance on one such processor is comparable to O(100) carefully programmed high-end PCs: it turns out to be even better for some selected spin models. We describe here codes that we are currently executing on the IANUS massively parallel FPGA-based system.

cond-mat.dis-nn↗

arXiv2005

Ianus: an Adpative FPGA Computer

Dedicated machines designed for specific computational algorithms can outperform conventional computers by several orders of magnitude. In this note we describe {\it Ianus}, a new generation FPGA based machine and its basic features: hardware integration and wide reprogrammability. Our goal is to build a machine that can fully exploit the performance potential of new generation FPGA devices. We also plan a software platform which simplifies its programming, in order to extend its intended range of application to a wide class of interesting and computationally demanding problems. The decision to develop a dedicated processor is a complex one, involving careful assessment of its performance lead, during its expected lifetime, over traditional computers, taking into account their performance increase, as predicted by Moore's law. We discuss this point in detail.

cond-mat.dis-nn↗

arXiv2004

Les Houches 'Physics at Tev Colliders 2003' QCD/SM Working Group: Summary Report

This report documents the results obtained by the Working Group on Quantum Chromodynamics and the Standard Model for the Workshop `Physics at TeV Colliders'', Les Houches, France, 26 May - 6 June 2003. After a Monte Guide description, the first contributions report on progress in describing multiple interactions, important for the LHC, and underlying events. An announcement of a Monte Carlo database, under construction, is then followed by a number of contributions improving parton shower descriptions. Subsequently, a large number of contributions address resummations in various forms, after which follow studies of QCD effects in pion pair, top quark pair and photon pair plus jet production. After a study of electroweak corrections to hadronic precision observables, the report ends by presenting recent progress in methods to compute finite order corrections at one-loop with many legs, and at two-loop.

hep-ph↗

arXiv2004

Phase diagram of the (bosonic) Double-Exchange Model

The phase diagram of the simplest approximation to Double-Exchange systems, the bosonic Double-Exchange model with antiferromagnetic super-exchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions and Variational Mean-Field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segment like ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase-transition, only short-range ordering would be found in neutron-scattering. Researchers looking for a Quantum Critical Point in manganites should be wary of this possibility. Finite-Size Scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

cond-mat.str-el↗