arXiv subjects

D. Navarro

Publications and source records attributed to D. Navarro.

At least 19 recordsLinked to original sources

arXiv2023

Quantifying memory in spin glasses

Rejuvenation and memory, long considered the distinguishing features of spin glasses, have recently been proven to result from the growth of multiple length scales. This insight, enabled by simulations on the Janus~II supercomputer, has opened the door to a quantitative analysis. We combine numerical simulations with comparable experiments to introduce two coefficients that quantify memory. A third coefficient has been recently presented by Freedberg et al. We show that these coefficients are physically equivalent by studying their temperature and waiting-time dependence.

cond-mat.dis-nn↗

arXiv2023

Multifractality in spin glasses

We unveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

cond-mat.dis-nn↗

arXiv2022

On the superposition principle and non-linear response in spin glasses

The extended principle of superposition has been a touchstone of spin glass dynamics for almost thirty years. The Uppsala group has demonstrated its validity for the metallic spin glass, CuMn, for magnetic fields $H$ up to 10 Oe at the reduced temperature $T_\mathrm{r}=T/T_\mathrm{g} = 0.95$, where $T_\mathrm{g}$ is the spin glass condensation temperature. For $H > 10$ Oe, they observe a departure from linear response which they ascribe to the development of non-linear dynamics. The thrust of this paper is to develop a microscopic origin for this behavior by focusing on the time development of the spin glass correlation length, $\xi(t,t_\mathrm{w};H)$. Here, $t$ is the time after $H$ changes, and $t_\mathrm{w}$ is the time from the quench for $T>T_\mathrm{g}$ to the working temperature $T$ until $H$ changes. We connect the growth of $\xi(t,t_\mathrm{w};H)$ to the barrier heights $\Delta(t_\mathrm{w})$ that set the dynamics. The effect of $H$ on the magnitude of $\Delta(t_\mathrm{w})$ is responsible for affecting differently the two dynamical protocols associated with turning $H$ off (TRM, or thermoremanent magnetization) or on (ZFC, or zero field-cooled magnetization). In this paper, we display the difference between the zero-field cooled $\xi_{\text {ZFC}}(t,t_\mathrm{w};H)$ and the thermoremanent magnetization $\xi_{\text {TRM}}(t,t_\mathrm{w};H)$ correlation lengths as $H$ increases, both experimentally and through numerical simulations, corresponding to the violation of the extended principle of superposition in line with the finding of the Uppsala Group.

cond-mat.dis-nn↗

arXiv2022

Memory and rejuvenation in spin glasses: aging systems are ruled by more than one length scale

Memory and rejuvenation effects in the magnetic response of off-equilibrium spin glasses have been widely regarded as the doorway into the experimental exploration of ultrametricity and temperature chaos (maybe the most exotic features in glassy free-energy landscapes). Unfortunately, despite more than twenty years of theoretical efforts following the experimental discovery of memory and rejuvenation, these effects have thus far been impossible to simulate reliably. Yet, three recent developments convinced us to accept this challenge: first, the custom-built Janus II supercomputer makes it possible to carry out "numerical experiments" in which the very same quantities that can be measured in single crystals of CuMn are computed from the simulation, allowing for parallel analysis of the simulation/experiment data. Second, Janus II simulations have taught us how numerical and experimental length scales should be compared. Third, we have recently understood how temperature chaos materializes in aging dynamics. All three aspects have proved crucial for reliably reproducing rejuvenation and memory effects on the computer. Our analysis shows that (at least) three different length scales play a key role in aging dynamics, while essentially all theoretical analyses of the aging dynamics emphasize the presence and the crucial role of a single glassy correlation length.

cond-mat.dis-nn↗

arXiv2021

Spin-glass dynamics in the presence of a magnetic field: exploration of microscopic properties

The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature $T_\mathrm{g}$. The spin-glass correlation length, $ξ(t,t_\mathrm{w};T)$, is analysed both in experiments and in simulations in terms of the waiting time $t_\mathrm{w}$ after the spin glass has been cooled down to a stabilised measuring temperature $T<T_\mathrm{g}$ and of the time $t$ after the magnetic field is changed. This correlation length is extracted experimentally for a CuMn 6 at. % single crystal, as well as for simulations on the Janus II special-purpose supercomputer, the latter with time and length scales comparable to experiment. The non-linear magnetic susceptibility is reported from experiment and simulations, using $ξ(t,t_\mathrm{w};T)$ as the scaling variable. Previous experiments are reanalysed, and disagreements about the nature of the Zeeman energy are resolved. The growth of the spin-glass magnetisation in zero-field magnetisation experiments, $M_\mathrm{ZFC}(t,t_\mathrm{w};T)$, is measured from simulations, verifying the scaling relationships in the dynamical or non-equilibrium regime. Our preliminary search for the de Almeida-Thouless line in $D=3$ is discussed.

cond-mat.dis-nn↗

arXiv2020

Scaling law describes the spin-glass response in theory, experiments and simulations

The correlation length $ξ$, a key quantity in glassy dynamics, can now be precisely measured for spin glasses both in experiments and in simulations. However, known analysis methods lead to discrepancies either for large external fields or close to the glass temperature. We solve this problem by introducing a scaling law that takes into account both the magnetic field and the time-dependent spin-glass correlation length. The scaling law is successfully tested against experimental measurements in a CuMn single crystal and against large-scale simulations on the Janus II dedicated computer.

cond-mat.stat-mech↗

arXiv2020

Temperature chaos is present in off-equilibrium spin-glass dynamics

We find a dynamic effect in the non-equilibrium dynamics of a spin glass that closely parallels equilibrium temperature chaos. This effect, that we name dynamic temperature chaos, is spatially heterogeneous to a large degree. The key controlling quantity is the time-growing spin-glass coherence length. Our detailed characterization of dynamic temperature chaos paves the way for the analysis of recent and forthcoming experiments. This work has been made possible thanks to the most massive simulation to date of non-equilibrium dynamics, carried out on the Janus~II custom-built supercomputer.

cond-mat.dis-nn↗

arXiv2019

The Mpemba effect in spin glasses is a persistent memory effect

The Mpemba effect occurs when a hot system cools faster than an initially colder one, when both are refrigerated in the same thermal reservoir. Using the custom built supercomputer Janus II, we study the Mpemba effect in spin glasses and show that it is a non-equilibrium process, governed by the coherence length ξof the system. The effect occurs when the bath temperature lies in the glassy phase, but it is not necessary for the thermal protocol to cross the critical temperature. In fact, the Mpemba effect follows from a strong relationship between the internal energy and ξthat turns out to be a sure-tell sign of being in the glassy phase. Thus, the Mpemba effect presents itself as an intriguing new avenue for the experimental study of the coherence length in supercooled liquids and other glass formers.

cond-mat.dis-nn↗

arXiv2019

Gas phase Elemental abundances in Molecular cloudS (GEMS) I. The prototypical dark cloud TMC 1

GEMS is an IRAM 30m Large Program whose aim is determining the elemental depletions and the ionization fraction in a set of prototypical star-forming regions. This paper presents the first results from the prototypical dark cloud TMC 1. Extensive millimeter observations have been carried out with the IRAM 30m telescope (3mm and 2mm) and the 40m Yebes telescope (1.3cm and 7mm) to determine the fractional abundances of CO, HCO+, HCN, CS, SO, HCS+, and N2H+ in three cuts which intersect the dense filament at the well-known positions TMC 1-CP, TMC 1-NH3, and TMC 1-C, covering a visual extinction range from Av~3 to ~20mag. Two phases with differentiated chemistry can be distinguished: i) the translucent envelope with molecular hydrogen densities of (1-5)x10$^3$ cm$^{-3}$; and ii) the dense phase, located at Av>10mag, with molecular hydrogen densities >10$^4$ cm$^{-3}$. Observations and modeling show that the gas phase abundances of C and O progressively decrease along the C+/C/CO transition zone where C/H~8x10$^{-5}$ and C/O~0.8-1, until the beginning of the dense phase at Av~10 mag. This is consistent with the grain temperatures being below the CO evaporation temperature in this region. In the case of sulfur, a strong depletion should occur before the translucent phase where we estimate a S/H~(0.4 - 2.2) x10$^{-6}$, an abundance ~7-40 times lower than the solar value. A second strong depletion must be present during the formation of the thick icy mantles to achieve the values of S/H measured in the dense cold cores (S/H~8x10$^{-8}$). Based on our chemical modeling, we constrain the value of $ζ_{\rm H_2}$ to ~(0.5 - 1.8) x10$^{-16}$ s$^{-1}$ in the translucent cloud.

astro-ph.GA↗

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↗

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↗

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↗