arXiv subjects

E. Marinari

Publications and source records attributed to E. Marinari.

At least 19 recordsLinked to original sources

arXiv2025

Microcanonical simulated annealing: Massively parallel Monte Carlo simulations with sporadic random-number generation

Numerical simulations of models and theories that describe complex systems such as spin glasses are becoming increasingly important. Beyond fundamental research, these computational methods also find practical applications in fields like combinatorial optimization. However, Monte Carlo simulations, an important subcategory of these methods, are plagued by a major drawback: they are extremely greedy for (pseudo) random numbers. The total fraction of computer time dedicated to random-number generation increases as the hardware grows more sophisticated, and can get prohibitive for special-purpose computing platforms. We propose here a general-purpose microcanonical simulated annealing (MicSA) formalism that dramatically reduces such a burden. The algorithm is fully adapted to a massively parallel computation, as we show in the particularly demanding benchmark of the three-dimensional Ising spin glass. We carry out very stringent numerical tests of the new algorithm by comparing our results, obtained on GPUs, with high-precision standard (i.e., random-number-greedy) simulations performed on the Janus II custom-built supercomputer. In those cases where thermal equilibrium is reachable (i.e., in the paramagnetic phase), both simulations reach compatible values. More significantly, barring short-time corrections, a simple time rescaling suffices to map the MicSA off-equilibrium dynamics onto the results obtained with standard simulations.

cond-mat.stat-mech↗

arXiv2024

Spin-glass dynamics: experiment, theory and simulation

The study of spin-glass dynamics, long considered the paradigmatic complex system, has reached important milestones. The availability of single crystals has allowed the experimental measurement of spin-glass coherence lengths of almost macroscopic dimensions, while the advent of special-purpose computers enables dynamical simulations that approach experimental scales. This review provides an account of the quantitative convergence of these two avenues of research, with precise experimental measurements of the expected scaling laws and numerical reproduction of classic experimental results, such as memory and rejuvenation. The article opens with a brief review of the defining spin-glass properties, randomness and frustration, and their experimental consequences. These apparently simple characteristics are shown to generate rich and complex physics. Models are introduced that enable quantitative dynamical descriptions. After a summary of the main numerical results in equilibrium, paying particular attention to temperature chaos, this review examines off-equilibrium dynamics in the absence of a magnetic field and shows how it can be related to equilibrium structures through the fluctuation-dissipation relations. The nonlinear response at a given temperature is then developed, including experiments and scaling in the vicinity of the transition temperature $T_\mathrm{g}$. The consequences of temperature change $\unicode{x2013}$including temperature chaos, rejuvenation, and memory$\unicode{x2013}$ are reviewed. The interpretation of these phenomena requires identifying several length scales relevant to dynamics, which, in turn, generate new insights. Finally, issues for future investigations are introduced, including what is to be nailed down theoretically, why the Ising Edwards-Anderson model is so successful at modeling spin-glass dynamics, and experiments yet to be undertaken.

cond-mat.dis-nn↗

arXiv2024

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↗

arXiv2024

Multiscaling in the 3D critical site-diluted Ising ferromagnet

We have studied numerically the appearance of multiscaling behavior in the three-dimensional ferromagnetic Ising site diluted model, in the form of a multifractal distribution of the decay exponents for the spatial correlation functions at the critical temperature. We have computed the exponents of the long-distance decay of higher moments of the correlation function, up to the 10th power, by studying three different quantities: global susceptibilities, local susceptibilities and correlation functions. We have found very clear evidences for multiscaling behavior.

cond-mat.dis-nn↗

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

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, $ξ(t,t_\mathrm{w};H)$. 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 $ξ(t,t_\mathrm{w};H)$ to the barrier heights $Δ(t_\mathrm{w})$ that set the dynamics. The effect of $H$ on the magnitude of $Δ(t_\mathrm{w})$ 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 $ξ_{\text {ZFC}}(t,t_\mathrm{w};H)$ and the thermoremanent magnetization $ξ_{\text {TRM}}(t,t_\mathrm{w};H)$ 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↗

arXiv2022

Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator

The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally-relevant model of such a system -- the so-called Brownian gyrator -- a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under non-equilibrium conditions, while no net rotation takes place in equilibrium. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components, but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in non-equilibrium. We show that indeed one can conclusively distinguish between equilibrium and non-equilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a non-equilibrium dynamics.

cond-mat.stat-mech↗

arXiv2021

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↗

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↗

arXiv2021

How we are leading a 3-XORSAT challenge: from the energy landscape to the algorithm and its efficient implementation on GPUs

A recent 3-XORSAT challenge required to minimize a very complex and rough energy function, typical of glassy models with a random first order transition and a golf course like energy landscape. We present the ideas beyond the quasi-greedy algorithm and its very efficient implementation on GPUs that are allowing us to rank first in such a competition. We suggest a better protocol to compare algorithmic performances and we also provide analytical predictions about the exponential growth of the times to find the solution in terms of free-energy barriers.

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

Dimensional crossover in the aging dynamics of spin glasses in a film geometry

Motivated by recent experiments of exceptional accuracy, we study numerically the spin-glass dynamics in a film geometry. We cover all the relevant time regimes, from picoseconds to equilibrium, at temperatures at and below the 3D critical point. The dimensional crossover from 3D to 2D dynamics, that starts when the correlation length becomes comparable to the film thickness, consists of four dynamical regimes. Our analysis, based on a Renormalization Group transformation, finds consistent the overall physical picture employed by Orbach et al. in the interpretation of their experiments.

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

An experiment-oriented analysis of 2D spin-glass dynamics: a twelve time-decades scaling study

Recent high precision experimental results on spin-glass films ask for a detailed understanding of the domain-growth dynamics of two-dimensional spin glasses. To achieve this goal, we numerically simulate the out-equilibrium dynamics of the Ising spin glass for a time that spans close to twelve orders of magnitude (from picoseconds to order of a second), in systems large enough to avoid finite-size effects. We find that the time-growth of the size of the glassy domains is excellently described by a single scaling function. A single time-scale $τ(T)$ controls the dynamics. $τ(T)$ diverges upon approaching the $T=0$ critical point. The divergence of $τ(T\to 0)$ is Arrhenius-like, with a barrier height that depends very mildly on temperature. The growth of this barrier-height is best described by critical dynamics. As a side product we obtain an impressive confirmation of universality of the equilibrium behavior of two-dimensional spin-glasses.

cond-mat.dis-nn↗

arXiv2019

The Essential Role of Thermodynamics in metabolic network modeling: physical insights and computational challenges

Quantitative studies of cell metabolism are often based on large chemical reaction network models. A steady state approach is suited to analyze phenomena on the timescale of cell growth and circumvents the problem of incomplete experimental knowledge on kinetic laws and parameters, but it shall be supported by a correct implementation of thermodynamic constraints. In this article we review the latter aspect highlighting its computational challenges and physical insights. The simple introduction of Gibbs inequalities avoids the presence of unfeasible loops allowing for correct timescale analysis but leads to possibly non-convex feasible flux spaces, whose exploration needs efficient algorithms. We shorty review on the implementation of thermodynamics through variational principles in constraints based models of metabolic networks.

q-bio.MN↗

arXiv2019

Spectral content of a single non-Brownian trajectory

Time-dependent processes are often analysed using the power spectral density (PSD), calculated by taking an appropriate Fourier transform of individual trajectories and finding the associated ensemble-average. Frequently, the available experimental data sets are too small for such ensemble averages, and hence it is of a great conceptual and practical importance to understand to which extent relevant information can be gained from $S(f,T)$, the PSD of a single trajectory. Here we focus on the behavior of this random, realization-dependent variable, parametrized by frequency $f$ and observation-time $T$, for a broad family of anomalous diffusions---fractional Brownian motion (fBm) with Hurst-index $H$---and derive exactly its probability density function. We show that $S(f,T)$ is proportional---up to a random numerical factor whose universal distribution we determine---to the ensemble-averaged PSD. For subdiffusion ($H<1/2$) we find that $S(f,T)\sim A/f^{2H+1}$ with random-amplitude $A$. In sharp contrast, for superdiffusion $(H>1/2)$ $S(f,T)\sim BT^{2H-1}/f^2$ with random amplitude $B$. Remarkably, for $H>1/2$ the PSD exhibits the same frequency-dependence as Brownian motion, a deceptive property that may lead to false conclusions when interpreting experimental data. Notably, for $H>1/2$ the PSD is ageing and is dependent on $T$. Our predictions for both sub- and superdiffusion are confirmed by experiments in live cells and in agarose hydrogels, and by extensive simulations.

cond-mat.stat-mech↗

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.

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