Nonequilibrium spin glass dynamics from picoseconds to 0.1 seconds
F. Belletti, M. Cotallo, A. Cruz, L. A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, A. Munoz Sudupe, … 展开作者
F. Belletti, M. Cotallo, A. Cruz, L. A. Fernandez, A. Gordillo-Guerrero, M. Guidetti, A. Maiorano, F. Mantovani, E. Marinari, V. Martin-Mayor, A. Munoz Sudupe, D. Navarro, G. Parisi, S. Perez-Gaviro, J. J. Ruiz-Lorenzo, S. F. Schifano, D. Sciretti, A. Tarancon, R. Tripiccione, J. L. Velasco, D. Yllanes
备注：
4 pages, 4 eps color figures. Version accepted for publication in Phys. Rev. Lett
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.
Nonequilibrium dynamics of the $\pm J$ Ising, the {\it XY}, and the Heisenberg spin-glass models are investigated in three dimensions. A nonequilibrium dynamic exponent is calculated from the dynamic correlation length. The spin-glass dynamic exponent continuously depends on the temperature. There is no anomaly at the critical temperature as is recently reported by Katzgraber and Campbell. On the other hand, the chiral-glass dynamic exponent takes a constant value above the spin-glass transition temperature ($T_\mathrm{sg}$), and becomes temperature-dependent below $T_\mathrm{sg}$.The finite-t…
The applications of nonequilbrium relations such as the Jarzynski equality and the fluctuation theorem to spin glasses are considered. The spin glass is a basic platform where we consider an application of an approximate solver of combinatorial optimization problems, simulated annealing. We find a novel relationship between an average through a nonequilibrium process where the temperature changes as in simulated annealing and a thermal average in equilibrium with different amounts of quenched randomness. The results shown in the present study may serve as an alternative way to overcome critica…
We employ Monte Carlo simulations to investigate the two-time density autocorrelation function for the two-dimensional Coulomb glass. We find that the nonequilibrium relaxation properties of this highly correlated disordered system can be described by a full aging scaling ansatz. The scaling exponents are non-universal, and depend on temperature and charge density.
The non-equilibrium dynamics of the three-dimensional Edwards-Anderson spin-glass model with different bond distributions is investigated by means of Monte Carlo simulation. A numerical method is used to determine the critical temperature and the scaling exponents of the correlation and the integrated response functions. The results obtained agree with those calculated in equilibrium simulations and suggest that the universality class does not depend on the exact form of the bond distribution.
The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature which is less than the spin glass transition temperature the ac susceptibility decreases with time elapsed after the initial quench towards equilibrium approximately logarithmically. It is shown that the transverse field of "tunneling" has nonessential effect to a non…
We study the non-equilibrium aging behavior of the gauge glass model in three dimensions at the critical temperature. We perform Monte Carlo simulations with a Metropolis update, and correlation and response functions are calculated for different waiting times. We obtain a multiplicative aging scaling of the correlation and response functions, calculating the aging exponent $b$ and the nonequilibrium autocorrelation decay exponent $λ_c/z_c$. We also analyze the fluctuation-dissipation relationship at the critical temperature, obtaining the critical fluctuation-dissipation ratio $X_\infty$. By …
The relaxations of conductivity have been studied in the glassy regime of a strongly disordered two-dimensional electron system in Si after a temporary change of carrier density during the waiting time t_w. Two types of response have been observed: a) monotonic, where relaxations exhibit aging, i.e. dependence on history, determined by t_w and temperature; b) nonmonotonic, where a memory of the sample history is lost. The conditions that separate the two regimes have been also determined.
We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing …
We numerically study the three-dimensional Edwards-Anderson model with Gaussian couplings, focusing on the heterogeneities arising in its nonequilibrium dynamics. Results are analyzed in terms of the backbone picture, which links strong dynamical heterogeneities to spatial heterogeneities emerging from the correlation of local rigidity of the bond network. Different two-times quantities as the flipping time distribution and the correlation and response functions, are evaluated over the full system and over high- and low-rigidity regions. We find that the nonequilibrium dynamics of the model is…
We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in the first large-scale simulation of the nonequilibrium dynamics of the three dimensional Heisenberg spin glass.
We have studied numerically the dynamics of spin glasses with Ising and XY symmetry (gauge glass) in space dimensions 2, 3, and 4. The nonequilibrium spin-glass susceptibility and the nonequilibrium energy per spin of samples of large size L_b are measured as a function of anneal time t_w after a quench to temperatures T. The two observables are compared to the equilibrium spin-glass susceptibility and the equilibrium energy, respectively, measured as functions of temperature T and system size L for a range of system sizes. For any time and temperature a nonequilibrium time-dependent length sc…
Motivated by short-range Ising spin glasses, we review some rigorous results and their consequences for the relation between the number/nature of equilibrium pure states and nonequilibrium dynamics. Two of the consequences for spin glass dynamics following a deep quench to a temperature with broken spin flip symmetry are: (1) Almost all initial configurations lie on the boundary between the basins of attraction of multiple pure states. (2) Unless there are uncountably many pure states with almost all pairs having zero overlap, there can be no equilibration to a pure state as time goes to infin…
We report on results of nonequilibrium transport measurements made on thin films of germanium-telluride (Ge_xTe) at cryogenic temperatures. Owing to a rather large deviation from stoichiometry (app. 10% of Ge vacancies), these films exhibit p-type conductivity with carrier-concentration N>10^20cm^(-3) and can be made either in the diffusive or strongly-localized regime by a judicious choice of preparation and post-treatment conditions. In both regimes the system shows persistent photoconductivity following excitation by a brief exposure to infrared radiation. Persistent photoconductivity is al…
We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for al…
Metallic glasses exhibit fast mechanical relaxations at temperatures well below the glass transition, one of which shows little variation with temperature known as nearly constant loss (NCL). Despite the important implications of this phenomenon to in aging and deformation, the origin of the relaxation is unclear. Through molecular dynamics simulations of a model metallic glass, Cu_64.5Zr_35.5, we implement dynamic mechanical analysis with system stress decomposed into atomic-level stresses to identify the group of atoms responsible for NCL. This work demonstrates that NCL relaxation is due to…
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 Edward…
The critical behavior of the gauge-glass and the XY spin-glass models in three dimensions is studied by analyzing their nonequilibrium aging dynamics. A new numerical method, which relies on the calculation of the two-time correlation and integrated response functions, is used to determine both the critical temperature and the nonequilibrium scaling exponents, both for spin and chiral degrees of freedom. First, the ferromagnetic XY model is studied to validate this nonequilibirum aging method (NAM), since for this nondisordered system we can compare with known results obtained with standard eq…
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.
A mean-field multi-spin interaction spin glass model is analyzed in the presence of a ferromagnetic coupling. The static and dynamical phase diagrams contain four phases (paramagnet, spin glass, ordinary ferromagnet and glassy ferromagnet) and exhibit reentrant behavior. The glassy ferromagnet phase has anomalous dynamical properties. The results are consistent with a nonequilibrium thermodynamics that has been proposed for glasses.
We present a mean field model for spin glasses with a natural notion of distance built in, namely, the Edwards-Anderson model on the diluted D-dimensional unit hypercube in the limit of large D. We show that finite D effects are strongly dependent on the connectivity, being much smaller for a fixed coordination number. We solve the non trivial problem of generating these lattices. Afterwards, we numerically study the nonequilibrium dynamics of the mean field spin glass. Our three main findings are: (i) the dynamics is ruled by an infinite number of time-sectors, (ii) the aging dynamics consist…
Dynamical systems of the gauge glass are investigated by the method of the gauge transformation.Both stochastic and deterministic dynamics are treated. Several exact relations are derived among dynamical quantities such as equilibrium and nonequilibrium auto-correlation functions, relaxation functions of order parameter and internal energy. They provide physical properties in terms of dynamics in the SG phase, a possible mixed phase and the Griffiths phase, the multicritical dynamics and the aging phenomenon. We also have a plausible argument for the absence of re-entrant transition in two or …
A three-dimensional $\pm J$ XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider tha…
Localisation-protected quantum order extends the idea of symmetry breaking and order in ground states to individual eigenstates at arbitrary energy. Examples include many-body localised static and $π$-spin glasses in Floquet systems. Such order is inherently dynamical and difficult to detect as the order parameter typically varies randomly between different eigenstates, requiring specific superpositions of eigenstates to be targeted by the initial state. We show that two-time correlators overcome this, reflecting the presence or absence of eigenstate order even in fully-mixed, $infinite$ $temp…
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 …
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field into inergodic spin glass phase with a number of metastable states. The thermodynamic properties of metastable states are studied at T=0 and near the transition. The relations between the characteristics of slow nonequilibrium processes in spin glass phase (such as hysteresis loop form, thermo-remanent and isothermal remanent magnetizations, field-cooled and z…
The field-cooled (FC) process on an Ising spin-glass model is investigated by a standard Monte Calro (MC) method on one hand, and the equilibrium magnetization of the same system is evaluated by the exchang MC method on the other hand. The two types of simulation reveal intriguing glassy (nonequilibrium) dynamic properties of the FC magnetization (FCM) of the system. Particularly, the FCM decrease is observed when the FC process is halted at a low temperater, although its value is smaller than the corresponding equilibrium value. We present a comprehensive interpretation of such peculiar pheno…
We find a possibility of a weak universality of spin-glass phase transitions in three-dimensional $\pm J$ models. The Ising, the XY and the Heisenberg models seem to undergo finite-temperature phase transitions with a ratio of the critical exponents $γ/ν\sim 2.4$. Evaluated critical exponents may explain corresponding experimental results. The analyses are based upon nonequilibrium relaxation from a paramagnetic state and finite-time scaling.
The dynamic behaviour of glassy materials displays strong nonequilibrium effects, such as ageing in simple protocols, memory, rejuvenation and Kovacs effects in more elaborated experiments. We show that this phenomenology may be easily understood in the context of the nonequilibrium critical dynamics of non-disordered systems, the main ingredient being the existence of an infinite equilibrium correlation length. As an example, we analytically investigate the behaviour of the 2D XY model submitted to temperature protocols similar to experiments. This shows that typical glassy effects may be obt…
The effect of applied magnetic fields on the collective nonequilibrium dynamics of a strongly interacting Fe-C nanoparticle system has been investigated. It is experimentally shown that the magnetic aging diminishes to finally disappear for fields of moderate strength. The field needed to remove the observable aging behavior increases with decreasing temperature. The same qualitative behavior is observed in an amorphous metallic spin glass (Fe_{0.15}Ni_{0.85})_{75}P_{16}B_6Al_3.
A spin-glass transition has been investigated for a long time but we have not yet reached a conclusion due to difficulties in the simulations. They are slow dynamics, strong finite-size effects, and sample-to-sample dependences. We clarified that these difficulties are mainly caused by a competition between the spin-glass order and the boundary conditions. We also found that the spin-glass order grows fast and reaches the lattice boundary within a very short Monte Carlo step. A key to solve the difficulties is to eliminate the boundary effect first. It was made possible by a dynamic scaling an…
Effects of temperature changes on the nonequilibrium spin-glass dynamics of a strongly interacting ferromagnetic nanoparticle system (superspin glass) are studied. In contrary to atomic spin glasses, strong cooling rate effects are observed, and no evidence for temperature-chaos is found. The flip time of a magnetic moment is much longer than that of an atomic spin and hence much shorter time scales are probed within the experimental time window for a superspin glass than for an atomic spin glass. Within a real space picture the cumulative aging observed for the superspin glass can be explaine…
We have studied the nonequilibrium dynamics of spin glasses subjected to bond perturbation, which was based on the direct change in the spin-spin interaction $ΔJ$, using photo illumination in addition to temperature change $ΔT$. Differences in time-dependent magnetization are observed between that under $ΔT+ΔJ$ and $ΔT$ perturbations with the same $ΔT$. This differences shows the contribution of $ΔJ$ to spin-glass dynamics through the decrease in the overlap length. That is, the overlap length $L_{ΔT+ΔJ}$ under $ΔT+ΔJ$ perturbation is less than $L_{ΔT}$ under $ΔT$ perturbation. Furthermore, we…
Temporal and spatial separations between spin glass and short-range order
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；California Institute of Technology（加州理工学院）
Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL-SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-…
We study numerically the nonequilibrium dynamics of the three-dimensional Heisenberg Edwards-Anderson spin glass submitted to protocols during which temperature is shifted or cycled within the spin glass phase. We show that (partial) rejuvenation and (perfect) memory effects can be numerically observed and study both effects in detail. We quantitatively characterize their dependences on parameters such as the amplitude of the temperature changes, the timescale at which the changes are performed, and the cooling rates used to vary the temperature. We contrast our results both to those found num…
We examine in this work the role of disorder in contributing to the sluggish relaxation observed in intrinsic electron-glasses. Our approach is guided by several empirical observations: First and foremost, Anderson localization is a pre-requisite for observing these nonequilibrium phenomena. Secondly, sluggish relaxation appears to favor Anderson-insulators with relatively large Fermi-energies (hence proportionally large disorder). These observations motivated us to consider a way to measure the underlying disorder in a realistic Anderson insulator. Optical study using a series of amorphous in…
We study the long-time aging dynamics of spin-glass models with two-spin interactions by performing a Renormalization Group transformation on the time variable in the non-equilibrium dynamical generating functional. We obtain the RG equations and find that the flow converges to an exact fixed point. We show that this fixed point is invariant under reparametrizations of the time variable. This continuous symmetry is broken, as evidenced by the fact that the observed correlations and responses are not invariant under it. We argue that this gives rise to the presence of Goldstone modes, and that …
We use large-scale molecular dynamics simulations of a simple glass-forming system to investigate how its liquid-gas phase separation kinetics depends on temperature. A shallow quench leads to a fully demixed liquid-gas system whereas a deep quench makes the dense phase undergo a glass transition and become an amorphous solid. This glass has a gel-like bicontinuous structure that evolves very slowly with time and becomes fully arrested in the limit where thermal fluctuations become negligible. We show that the phase separation kinetics changes qualitatively with temperature, the microscopic dy…
The anisotropic spin glass transition, in which spin freezing is observed only along the c-axis in pseudobrookite Fe$_2$TiO$_5$, has long been perplexing because the Fe$^{3+}$ moments (d$^5$) are expected to be isotropic. Recently, neutron diffraction demonstrated that surfboard-shaped antiferromagnetic nanoregions coalesce above the glass transition temperature, T$_g$ $\approx$ 55 K, and a model was proposed in which the freezing of the fluctuations of the surfboards' magnetization leads to the anisotropic spin glass state. Given this new model, we have carried out high resolution inelastic n…
Active matter, whose motion is driven, and glasses, whose dynamics are arrested, seem to lie at opposite ends of the spectrum in nonequilibrium systems. In spite of this, both classes of systems exhibit a multitude of stable states that are dynamically isolated from one another. While this defining characteristic is held in common, its origin is different in each case: for active systems, the irreversible driving forces can produce dynamically frozen states, while glassy systems vitrify when they get kinetically trapped on a rugged free energy landscape. In a mixture of active and glassy parti…
Toyota Central R&D Labs, Inc.（丰田中央研发实验室股份有限公司）；Nagoya University（名古屋大学）
Glass transitions are widely observed in various types of soft matter systems. However, the physical mechanism of these transitions remains {elusive}, despite years of ambitious research. In particular, an important unanswered question is whether the glass transition is accompanied by a divergence of the correlation lengths of the characteristic static structures. In this study, we develop a deep-neural-network-based method that is used to extract the characteristic local meso-structures solely from instantaneous {particle} configurations without any {information} about the dynamics. We first …
