Nonequilibrium Spin-Glass Dynamics from Picoseconds to a Tenth of a Second

Belletti, F.; Cotallo, M.; Cruz, A.; Fernández, L. A.; Gordillo‐Guerrero, A.; Guidetti, M.; Maiorano, Andrea; Mantovani, Filippo; Marinari, Enzo; Martı́n-Mayor, V.; Sudupe, A. Muñoz; Navarro, D.; Parisi, G.; Pérez-Gaviro, S.; Ruiz‐Lorenzo, J. J.; Schifano, Sebastiano Fabio; Sciretti, D.; Tarancón, A.; Tripiccione, R.; Velasco, J. L.; Yllanes, David

doi:10.1103/physrevlett.101.157201

Cited by 86 publications

(195 citation statements)

References 40 publications

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“…Indeed, our previous non-equilibrium study [24,25] reached a time scale that corresponds to the present equilibrium L = 32 simulation. Yet, the numerical effort to obtain the data in Fig.…”

Section: Discussionmentioning

confidence: 66%

“…Of course, care must be exercised because C 4 in a finite lattice cannot be computed beyond r = L/2, while C 2+2 is defined for arbitrary r. However, the matching is very accurate, even for r dangerously close to L/2, see figure 17. It is interesting to point out that the off-equilibrium results of [24] and our equilibrium simulations have similar precision, even though the latter required about twenty times more computation time on Janus, not to mention a much more complicated simulation protocol. In this sense we arrive at the conclusion that simulating the dynamics may be the best way to obtain certain equilibrium quantities.…”

Section: Non-equilibrium Vs Equilibriummentioning

confidence: 61%

“…The evidence for this correspondence consists of: (i) quantitative comparison of the spatial correlation functions and (ii) the analysis of overlap equivalence on equilibrium (this work) and non-equilibrium settings [25]. In addition, there is a remarkable coincidence between the replicon exponent obtained from equilibrium methods [26], and from non-equilibrium dynamics [24,25].…”

Section: Discussionmentioning

confidence: 93%

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Nature of the spin-glass phase at experimental length scales

Baños¹,

Cruz²,

Fernández³

et al. 2010

J. Stat. Mech.

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Abstract. 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 ≈ 0.64T c . 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.

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“…Indeed, our previous non-equilibrium study [24,25] reached a time scale that corresponds to the present equilibrium L = 32 simulation. Yet, the numerical effort to obtain the data in Fig.…”

Section: Discussionmentioning

confidence: 66%

Section: Non-equilibrium Vs Equilibriummentioning

confidence: 61%

Section: Discussionmentioning

confidence: 93%

See 1 more Smart Citation

Nature of the spin-glass phase at experimental length scales

Baños¹,

Cruz²,

Fernández³

et al. 2010

J. Stat. Mech.

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“…The scenario of nonequilibrium relaxation discussed here characteristically differs from aging dynamics in spin glasses [35,36] or that following density quenches in hard spheres [37][38][39]. There the structural relaxation time τ (t w ) grows with sample age, so that correlation functions and related two-time averages depend on t w in their long-time part, while the short-time relaxation for increasing sample age reveals more and more of an intrinsic, t w -independent relaxation.…”

Section: (T )G(t T [γ]) Dt Where the Generalized Shear Modulus Gmentioning

confidence: 78%

Residual Stresses in Glasses

et al. 2013

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The history dependence of the glasses formed from flow-melted steady states by a sudden cessation of the shear rateγ is studied in colloidal suspensions, by molecular dynamics simulations, and modecoupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function ofγt, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables, but differing static properties.PACS numbers: 64.70. P-83.50.-v Materials are often produced by solidification from the melt, involving nonequilibrium quenches. This imprints a history-dependent microstructure that strongly affects macroscopic material properties. One example is residual stresses [1,2]: if particle configurations cannot fully relax to equilibrium, some of the stresses, arising in the presence of flow in the melt, persist in the solid.Small glass droplets (known as Prince Rupert's drops or Dutch tears since the 17th century) vividly display the effects of residual stresses [3]: they withstand the blow of a hammer onto their main body, but explode when the slightest damage is inflicted upon their tail (releasing the frozen-in stress network). Today, safety glass and "Gorilla glass" covers for smartphones are deliberately pre-stressed during production to strengthen them. A theoretical understanding of residual stresses and their microscopic origins is however still not achieved.We seek to understand generic mechanisms by which residual stresses arise. A convenient starting point is to investigate the stress relaxation σ(t) following the cessation of shear flow of rateγ, from a well-defined nonequilibrium stationary state (NESS). Such "mechanical quenches" are ubiquitous in soft matter, where pre-shear is applied to "rejuvenate" the otherwise ill-defined glassy state [4][5][6][7]. For these systems, the soft-glassy rheology model (SGR) [8] predicts asymptotic power laws that imply the relaxation of stresses to zero [9]. In the following, we will reserve the term residual stress to describe a finite, persistent stress remaining in the (ideal) glass even at arbitrarily large times after the cessation of flow.In addition to macroscopic rheology, we investigate the evolution of the microscopic dynamics as characterized by the waiting-time dependent mean-squared displacements (MSD). The latter reveal the dynamical shrinkage of shear-fluidized regions after cessation, and phenomena akin to, yet different from the intensely studied aging dynamics after thermal quenches [10,11].Experiments on a variety of colloidal suspensions, together with molecular-dynamics (MD) simulations, provide a coherent qualitative picture that can be rationalized by mode-coupling theory of the glass transition (MCT) [12] within the integration-through-transients (ITT) formalis...

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“…We encounter the numerical instability caused by the expression 0/0. In order to avoid this problem, Bellettiet al [3] proposed the reduction of this instability by estimating ξ through the integrals I k = 0 drr k f (r) and ξ is obtained as I 2 /I 1 . Suwa and Todo [4] proposed a generalized moment method for gap (∆ ∼ 1/ξ) estimation in quantum systems.…”

mentioning

confidence: 99%

From measurements to inferences of physical quantities in numerical simulations

Nakamura

2016

Phys. Rev. E

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We propose a change of style for numerical estimations of physical quantities from measurements to inferences. We estimate the most probable quantities for all the parameter region simultaneously by using the raw data cooperatively. Estimations with higher precisions are made possible. We can obtain a physical quantity as a continuous function, which is differentiated to obtain another quantity. We applied the method to the Heisenberg spin-glass model in three dimensions. A dynamic correlation-length scaling analysis suggests that the spin-glass and the chiral-glass transitions occur at the same temperature with a common exponent ν. The value is consistent with the experimental results. We found that a size-crossover effect explains a spin-chirality separation problem.Introduction-Estimations of physical quantities in numerical simulations are based on equilibrium statistical physics [1]. We virtualize a model system in a computer and perform independent measurements on the system using a definition of a physical quantity. When an evaluation process is complex, both systematic and statistical errors are accumulated in the obtained data. We sometimes encounter numerical instabilities, which may affect a final physical conclusion. In what follows, we explain the situation of interest using a correlation-length estimation.An estimation formula for a correlation length, ξ, is given by the second-moment method:. Here, χ 0 denotes the susceptibility and χ k its Fourier transform with k as the lowest wave number of the system. This expression itself is problematic. Both numerator and denominator of this expression approach zero as the system size increases (k → 0), where this formula becomes exact. We encounter the numerical instability caused by the expression 0/0. In order to avoid this problem, Bellettiet al. [3] proposed the reduction of this instability by estimating ξ through the integrals I k = 0 drr k f (r) and ξ is obtained as I 2 /I 1 . Suwa and Todo [4] proposed a generalized moment method for gap (∆ ∼ 1/ξ) estimation in quantum systems. Systematic errors and ambiguity caused by using small-L data are eliminated.Recently, big-data handling has become possible due to rapid increase in computational power. Data science is now one of the most promising fields in science and technology. As regards its application to physics, the topic of Bayesian inference has attracted considerable interest [5,6]. In this context, Harada [7] introduced Bayesian inference into a parameter estimation of the finite-size scaling analysis.In this paper, we extend its application to estimations of physical quantities. For example, we can obtain an analytic expression for an energy out of the discrete raw data as the most-probable model function. Then, we obtain the specific heat by analytically differentiating it. A critical temperture is estimated automatically within this procedure. Since directly-observed (raw) data are

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Nonequilibrium Spin-Glass Dynamics from Picoseconds to a Tenth of a Second

Cited by 86 publications

References 40 publications

Nature of the spin-glass phase at experimental length scales

Nature of the spin-glass phase at experimental length scales

Residual Stresses in Glasses

From measurements to inferences of physical quantities in numerical simulations

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