Spin Glasses

Beautiful theories of magnetic hysteresis based on random microscopic disorder have been developed over the past ten years. Our goal was to directly compare these theories with precise experiments. To do so, we first developed and then applied coherent x-ray speckle metrology to a series of thin multilayer perpendicular magnetic materials. To directly observe the effects of disorder, we deliberately introduced increasing degrees of disorder into our films. We used coherent x rays, produced at the Advanced Light Source at Lawrence Berkeley National Laboratory, to generate highly speckled magnetic scattering patterns. The apparently "random" arrangement of the speckles is due to the exact configuration of the magnetic domains in the sample. In effect, each speckle pattern acts as a unique fingerprint for the magnetic domain configuration. Small changes in the domain structure change the speckles, and comparison of the different speckle patterns provides a quantitative determination of how much the domain structure has changed. Our experiments quickly answered one longstanding question: How is the magnetic domain configuration at one point on the major hysteresis loop related to the configurations at the same point on the loop during subsequent cycles? This is called microscopic return-point memory ͑RPM͒. We found that the RPM is partial and imperfect in the disordered samples, and completely absent when the disorder is below a threshold level. We also introduced and answered a second important question: How are the magnetic domains at one point on the major loop related to the domains at the complementary point, the inversion symmetric point on the loop, during the same and during subsequent cycles? This is called microscopic complementary-point memory ͑CPM͒. We found that the CPM is also partial and imperfect in the disordered samples and completely absent when the disorder is not present. In addition, we found that the RPM is always a little larger than the CPM. We also studied the correlations between the domains within a single ascending or descending loop. This is called microscopic half-loop memory and enabled us to measure the degree of change in the domain structure due to changes in the applied field. No existing theory was capable of reproducing our experimental results. So we developed theoretical models that do fit our experiments. Our experimental and theoretical results set benchmarks for future work.

We present a simple model that allows hysteresis loops with exchange bias to be reproduced. The model is a modification of the Tϭ0 random-field Ising model driven by an external field and with synchronous local relaxation dynamics. The main novelty of the model is that a certain fraction f of the exchange constants between neighboring spins is enhanced to a very large value J E . The model allows the dependence of the exchange bias and other properties of the hysteresis loops to be analyzed as a function of the parameters of the model: the fraction f of enhanced bonds, the amount of the enhancement J E , and the amount of disorder, which is controlled by the width of the Gaussian distribution of the random fields.

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

We propose a new method to compute the configurational entropy of glassy systems as a function of the free energy of valleys at a given temperature, in the framework of the Stillinger and Weber approach. In this method, which we call free-energy inherent structures (FEIS) approach, valleys are represented by inherent structures that are statistically grouped according to their free-energy rather than the energy as is commonly done in the standard procedure. The FEIS method provides a further step toward a description of the relaxational behavior of glassy systems in terms of a free energy measure. It can be used to determine the character of the glass transition as well as the mode coupling and the Kauzmann temperatures. We illustrate the usefulness of the method by applying it to simple models of glasses and spin glasses.

Quantum computers are projected to handle the Gibbs sampling and the related inference on Markov networks effectively. Apart from noting the background information useful for those starting the explorations in this important thread of Quantum Machine Learning, we capture some results and observations obtained through extensive simulations with two popular paradigms of sampling based on Quantum Annealing and Quantum Approximate Optimization Algorithm.

A one-dimensional (1D) coordination polymer, [{Co 2 (pymca) , was solvothermally synthesized via the reaction of 2-cyanopyrimidine and Co(SCN) 2 . A bidentate pymca ligand was formed in situ by the hydrolysis of 2-cyanopyrimidine. Furthermore, in this study, the magnetic properties of complex 1 were investigated in detail. The results indicated that complex 1 showed a single-chain magnet (SCM) behavior below ca. 3 K. The energy barrier (Ds 1 /k B ) and preexponential factor (s 0 ) of SCM were 31.2 K and 5.4 Â 10 À9 s, respectively.

We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.

The relative volume of spin states in the phase space is introduced for the ±J model of spin glasses. Analysis of its temperature dependence shows that the Nishimori line separates the pure ferromagnetic-like region in the high-temperature side of the ferromagnetic phase from the randomness-dominated region in the low-temperature side. The peak value of the relative volume of the perfect ferromagnetic state is shown to be equivalent to the entropy. Upper and lower bounds on the entropy are derived, which determine the value of the entropy quite precisely.

In this work we study spin-glass (SG) like behavior in the dynamics of multiple agents in a social or economic context using interactions which are similar to the physical case. The different preferences shown by individual agents are represented by orientations of spin-like variables. Because of limited resources, each agent tries to maximize her total utility function, giving a prescription for the dynamics of the system similar to the evolution resulting from the optimization of the interaction of a SG. The coupling between agents for different attributes may be positive or negative, as in a physical SG system, forming "frustrations" from the ensuing conflicts, with the system trying to find an overall equilibrium, but in vain, so that we observe oscillations. The couplings are provided by matrices corresponding to each attribute and each agent, which are allowed to have some fixed bias, indicating the unchangeable component of the make up of the agents from genetic factors or lasting environmental influences, and also contain a random part from environmental noise, i.e. the cumulative stochastic effect of lumped factors not explicitly accounted for in the model. In a simulation of a small world with a small number of agents and attributes we observe, for particular choices of the coupling matrices, interesting variations of behavior patterns, including oscillations with different long and short term behavior of punctuated equilibria. We also show that if the "spin" variables are extended to become coordinate-like variables, the interaction appears like the distance function in differential geometry, with the coupling matrices forming an indefinite metric in the state space of the system. We comment on the relevance and consequences of equations of motion that may be derived from such an analogy.

Aging phenomena in complex systems has been used as an important tool to investigate the physics of complexity. In particular aging effects in spin glasses, measured using the Thermoremenant Magnetization (TRM) decays, have been instrumental as a probe of complex equilibrium and nonequilibrium dynamics. Current theoretical and experimental analysis suggest that the TRM decay of spin glasses is mainly composed of two terms; The "stationary" term which does not depend on the sample history and dominates the short time decay (<1s) and a long time aging term which depends on the samples history. We report finding that aging found in spin glass materials, has a finite lifetime and that after aging has ended there is a third component of the magnetization decay. This decay is independent of the waiting time, logarithmic in nature and part of the same mechanism that produces aging. Finally we find that the logarithmic decay implies a maximum aging time (MAT) that is very strongly dependent on temperature and ranges from short times near the spin glass transition temperature to many times the current best estimates of the age of the universe for low temperature.

Gradient Symbolic Computation is proposed as a means of solving discrete global optimization problems using a neurally plausible continuous stochastic dynamical system. Gradient symbolic dynamics involves two free parameters that must be adjusted as a function of time to obtain the global maximizer at the end of the computation. We provide a summary of what is known about the GSC dynamics for special cases of settings of the parameters, and also establish that there is a schedule for the two parameters for which convergence to the correct answer occurs with high probability. These results put the empirical results already obtained for GSC on a sound theoretical footing.

We investigate the critical behavior of a three-dimensional short-range spin glass model in the presence of an external field ǫ conjugated to the Edwards-Anderson order parameter. In the meanfield approximation this model is described by the Adam-Gibbs-DiMarzio approach for the glass transition. By Monte Carlo numerical simulations we find indications for the existence of a line of critical points in the plane (ǫ, T ) which separates two paramagnetic phases and terminates in a critical endpoint. This line of critical points appears due to the large degeneracy of metastable states present in the system (configurational entropy) and is reminiscent of the first-order phase transition present in the mean-field limit. We propose a scenario for the spin-glass transition at ǫ = 0, driven by a spinodal point present above Tc, which induces strong metastability through Griffiths singularities effects and induces the absence of a two-step shape relaxation curve characteristic of glasses.

Our systematic study has shown that the gap in doped CeNiSn Kondo insulator is very sensitive to the degree of hybridization V between the f-electron and conduction electron states. In the system CeNi 1Àx Rh x Sn, the carrier concentration diminishes upon Rh substitution for Ni. The transition from Kondo-insulator region to a metallic region is discussed as a function of variable valence electron number induced by substitution of Rh for Ni and of the accompanying effect of the change hybridization energy V.

We derive upper and lower bounds for the spectral gap of the random energy model under Metropolis dynamics which are sharp in exponential order. They are based on the variational characterization of the gap. For the lower bound, a Poincaré inequality derived by Diaconis and Stroock is used. The scaled asymptotic expression is a linear function of the temperature. The corresponding function for a global version of the dynamics exhibits phase transition instead. We also study the dependence of lower order terms on the volume. In the global dynamics, we observe a phase transition. For the local dynamics, the expressions we have, which are possibly not sharp, do not change their order of dependence on the volume as the temperature changes.

A "Kallen-Lehman" approach to Ising model, inspired by quantum field theory a la Regge, is proposed. The analogy with the Kallen-Lehman representation leads to a formula for the free-energy of the 3D model with few free parameters which could be matched with the numerical data. The possible application of this scheme to the spin glass case is shortly discussed.

We review some of the techniques used to study the dynamics of disordered systems subject to both quenched and fast (thermal) noise. Starting from the Martin-Siggia-Rose path integral formalism for a single variable stochastic dynamics, we provide a pedagogical survey of the perturbative, i.e. diagrammatic, approach to dynamics and how this formalism can be used for studying soft spin models. We review the supersymmetric formulation of the Langevin dynamics of these models and discuss the physical implications of the supersymmetry. We also describe the key steps involved in studying the disorder-averaged dynamics. Finally, we discuss the path integral approach for the case of hard Ising spins and review some recent developments in the dynamics of such kinetic Ising models.

Results of a Monte Carlo simulation appropriate to describe the compound Fe Zn F are consistent with spin-glass behavior at zero magnetic "eld and below the freezing temperature ¹. Binder cumulants, Edwards}Anderson parameter, and non-linear susceptibility, display critical-like behavior near ¹ , with exponents in agreement with those of stochastic models.

The distribution of interaction fields of an Ising-like system, obtained by Monte Carlo entropic sampling is used for modeling the hysteretic behavior of patterned media made of magnetic particles with a common anisotropy axis; a variant of the canonical Edwards-Anderson Ising spin glass model is introduced.

A nematic phase, previously seen in the d = 3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the hightemperature disordered phase, for number of spin components n 3, in spatial dimension d = 3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. Furthermore, under application of a variety of uniform magnetic fields, a veritable plethora of phases is found. Under uniform magnetic fields, 17 different phases and two spin-glass phase diagram topologies (meaning the occurrences and relative positions of the many phases), qualitatively different from the conventional spin-glass phase diagram topology, are seen. The chaotic rescaling behaviors and their Lyapunov exponents are calculated in each of these spin-glass phase diagram topologies. These results are obtained from renormalization-group calculations that are exact on the d = 3 hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. Axial, planar-diagonal, or body-diagonal finite-strength uniform fields are applied to n = 2 and 3 component cubic-spin spin-glass systems in d = 3.

The aging and memory effects of Fe3O4 nanoparticles have been studied using a series of zero-field cooled (ZFC) and field-cooled (FC) magnetization measurements at various aging protocols. The genuine ZFC magnetization after the ZFC procedure with a single stop and wait process shows an aging dip at the stop temperature on reheating. The depth of the aging dip is dependent on the wait time. The frequency dependence of the AC magnetic susceptibility is indicative of critical slowing down at a freezing temperature T f (= 30.6 ± 1.6 K). The relaxation time τ is described by a power law form with a dynamic critical exponent x (= 8.2 ± 1.0) and a microscopic relaxation time τ0 [= (1.33 ± 0.05) × 10 −9 sec]. The ZFC-peak temperature decreases with increasing magnetic field (H), forming a critical line with an exponent p = 1.78 ± 0.26, close to the de Almeida-Thouless exponent (p = 3/2). These results indicate that the superspin glass phase occurs below T f .

The anelastic spectra of La2−xSrxCuO4 have been measured at liquid He temperatures slightly below and above the concentration xc ≃ 0.02 which is considered to separate the spin-glass phase from the cluster spin-glass (CSG) phase. For x ≤ xc all the elastic energy loss functions show a step below the temperature Tg (x = 0.02) of freezing into the CSG state, similarly to what found in samples well within the CSG phase, but with a smaller amplitude. The excess dissipation in the CSG state is attributed to the motion of the domain walls between the clusters of antiferromagnetically correlated spin. These results are in agreement with the recent proposal, based on inelastic neutron scattering, of an electronic phase separation between regions with x ∼ 0 and x ∼ 0.02, at least for x > 0.015.

A complexity classification scheme is developed from the fractal spectra of spin-glass chaos and demonstrated with multigeographic multicultural music and brain electroencephalogram signals. Systematic patterns are found to emerge. Chaos under scale change is the essence of spin-glass ordering and can be obtained, continuously tailor-made, from the exact renormalization-group solution of Ising models on frustrated hierarchical lattices. The music pieces are from Turkish music, namely Arabesque, Rap, Pop, Classical, and Western music, namely Blues, Jazz, Pop, Classical. A surprising group defection occurs.

The anelastic spectra of La2−xSrxCuO4 have been measured at liquid He temperatures slightly below and above the concentration xc ≃ 0.02 which is considered to separate the spin-glass phase from the cluster spin-glass (CSG) phase. For x ≤ xc all the elastic energy loss functions show a step below the temperature Tg (x = 0.02) of freezing into the CSG state, similarly to what found in samples well within the CSG phase, but with a smaller amplitude. The excess dissipation in the CSG state is attributed to the motion of the domain walls between the clusters of antiferromagnetically correlated spin. These results are in agreement with the recent proposal, based on inelastic neutron scattering, of an electronic phase separation between regions with x ∼ 0 and x ∼ 0.02, at least for x > 0.015.

Carbon nanoclusters produced by high-repetition-rate laser ablation of graphite and glassy carbon in Ar exhibits para-and ferromagnetic behavior at low temperature. Magnetic susceptibility and electron paramagnetic resonance of carbon nanofoam samples produced at different Ar pressures demonstrate ferromagnetic behaviour at low temperatures. The results show that the degree of remanent order is strongly dependent on the magnetic history, i.e. whether the samples were cooled under zero-field or field conditions. Such behaviour is typical for a spin glass picture where the system can exist in many different roughly equivalent spin configurations. Detailed EPR studies identified three different types of independent spin systems with relaxation times 100 ns, 0.1-1 µs, and 1 ms. We conclude that unpaired spins exist in the nanofoam in three quite different structural environments. Their role in the magnetic ordering is discussed.

The distribution of the Fisher zeros in the Kallen-Lehman approach to three-dimensional Ising model is studied. It is argued that the presence of a non-trivial angle (a cusp) in the distribution of zeros in the complex temperatures plane near the physical singularity is realized through a strong breaking of the 2D Ising self-duality. Remarkably, the realization of the cusp in the Fisher distribution ultimately leads to an improvement of the results of the Kallen-Lehmann ansatz. In fact, excellent agreement with Monte Carlo predictions both at high and at low temperatures is observed. Besides, agreement between both approaches is found for the predictions of the critical exponent α and of the universal amplitude ratio ∆ =A+/A−, within the 3.5% and 7% of the Monte Carlo predictions, respectively.

Results of a Monte Carlo simulation appropriate to describe the compound Fe Zn F are consistent with spin-glass behavior at zero magnetic "eld and below the freezing temperature ¹. Binder cumulants, Edwards}Anderson parameter, and non-linear susceptibility, display critical-like behavior near ¹ , with exponents in agreement with those of stochastic models.

This paper considers a Gaussian channel with one transmitter and two receivers. The goal is to maximize the communication rate at the intended/primary receiver subject to a disturbance constraint at the unintended/secondary receiver. The disturbance is measured in terms of minimum mean square error (MMSE) of the interference that the transmission to the primary receiver inflicts on the secondary receiver. The paper presents a new upper bound for the problem of maximizing the mutual information subject to an MMSE constraint. The new bound holds for vector inputs of any length and recovers a previously known limiting (when the length for vector input tends to infinity) expression from the work of Bustin et al. The key technical novelty is a new upper bound on MMSE. This new bound allows one to bound the MMSE for all signal-to-noise ratio (SNR) values below a certain SNR at which the MMSE is known (which corresponds to the disturbance constraint). This new bound complements the ‘single...

A Kallen-Lehman approach to 3D Ising model is analyzed numerically both at low and high temperature. It is shown that, even assuming a minimal duality breaking, one can fix three parameters of the model to get a very good agreement with the MonteCarlo results at high temperatures. With the same parameters the agreement is satisfactory both at low and near critical temperatures. How to improve the agreement with Monte-Carlo results by introducing a more general duality breaking is shortly discussed.

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical p-spin model, which has the following advantages: 1) the Parisi Ansatz takes the simple "one step replica symmetry breaking form", 2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.

A nematic phase, previously seen in the 𝑑 = 3 classical Heisenberg spin-glass system, occurs in the n-component cubic-spin spin-glass system, between the low-temperature spin-glass phase and the-high temperature disordered phase, for number of components 𝑛 ≥ 3, in spatial dimension 𝑑 = 3, thus constituting a liquid-crystal phase in a dirty (quenched-disordered) magnet. This result is obtained from renormalization-group calculations that are exact on the hierarchical lattice and, equivalently, approximate on the cubic spatial lattice. The nematic phase completely intervenes between the spin-glass phase and the disordered phase. The Lyapunov exponents of the spin-glass chaos are calculated from 𝑛 = 1 up to 𝑛 = 12 and show odd-even oscillations with respect to 𝑛.

We study the low temperature out of equilibrium Monte Carlo dynamics of the disordered Ising p-spin Model with p = 3 and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers and trapping times on subsequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various Trap Models finding the best agreement with the Step Model when the p-spin configurations are constrained to be uncorrelated.

Recently we have used a cellular automata model which describes the dynamics of a multi-connected network to reproduce the refractory behavior and aging effects obtained in immunization experiments performed with mice when subjected to multiple perturbations. In this paper we investigate the similarities between the aging dynamics observed in this multi-connected network and the one observed in glassy systems, by using the usual tools applied to analyze the latter. An interesting feature we show here, is that the model reproduces the biological aspects observed in the experiments during the long transient time it takes to reach the stationary state. Depending on the initial conditions, and without any perturbation, the system may reach one of a family of long-period attractors. The perturbations may drive the system from its natural attractor to other attractors of the same family. We discuss the different roles played by the small random perturbations ("noise") and by the large periodic perturbations ("immunizations").

Spin glasses are experiencing a revival due to applications in quantum information theory. In particular, they are the archetypal native benchmark problem for quantum annealing machines. Furthermore, they find applications in fields as diverse as satisfiability, neural networks, and general combinatorial optimization problems. As such, developing v

Carbon nanoclusters produced by high-repetition-rate laser ablation of graphite and glassy carbon in Ar exhibits para-and ferromagnetic behavior at low temperature. Magnetic susceptibility and electron paramagnetic resonance of carbon nanofoam samples produced at different Ar pressures demonstrate ferromagnetic behaviour at low temperatures. The results show that the degree of remanent order is strongly dependent on the magnetic history, i.e. whether the samples were cooled under zero-field or field conditions. Such behaviour is typical for a spin glass picture where the system can exist in many different roughly equivalent spin configurations. Detailed EPR studies identified three different types of independent spin systems with relaxation times 100 ns, 0.1-1 µs, and 1 ms. We conclude that unpaired spins exist in the nanofoam in three quite different structural environments. Their role in the magnetic ordering is discussed.

Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an odor, and establish distributed memory that can be retrieved upon re-exposure. In contrast, the immune system encodes specialized memory by diverse receptors that recognize a multitude of evolving pathogens. Despite the mechanistic differences between the olfactory and the immune memory, these systems can still be viewed as different information encoding strategies. Here, we present a theoretical framework with artificial neural networks to characterize optimal memory strategies for both static and dynamic (evolving) patterns. Our approach is a generalization of the energy-based Hopfield model in which memory is stored as a network's energy minima. We find that while classical Hopfield networks with distributed memory can efficiently encode a memory of static patterns, they are inadequate against evolving patterns. To follow an evolving pattern, we show that a distributed network should use a higher learning rate, which in turn, can distort the energy landscape associated with the stored memory attractors. Specifically, narrow connecting paths emerge between memory attractors, leading to misclassification of evolving patterns. We demonstrate that compartmentalized networks with specialized subnetworks are the optimal solutions to memory storage for evolving patterns. We postulate that evolution of pathogens may be the reason for the immune system to encoded a focused memory, in contrast to the distributed memory used in the olfactory cortex that interacts with mixtures of static odors.

We discuss the set of pure states of some models which are ordered in a non-periodic way. This includes some results on a random model and some based on the Thue-Morse system. We discuss the possible nature of non-periodic long-range order, and also the overlap distribution between the pure states.

One of the hallmarks of biological organisms is their ability to integrate disparate information sources to optimize their behavior in complex environments. How this capability can be quantified and related to the functional complexity of an organism remains a challenging problem, in particular since organismal functional complexity is not well-defined. We present here several candidate measures that quantify information and integration, and study their dependence on fitness as an artificial agent ("animat") evolves over thousands of generations to solve a navigation task in a simple, simulated environment. We compare the ability of these measures to predict high fitness with more conventional information-theoretic processing measures. As the animat adapts by increasing its "fit" to the world, information integration and processing increase commensurately along the evolutionary line of descent. We suggest that the correlation of fitness with information integration and with processing measures implies that high fitness requires both information processing as well as integration, but that information integration may be a better measure when the task requires memory. A correlation of measures of information integration (but also information processing) and fitness strongly suggests that these measures reflect the functional complexity of the animat, and that such measures can be used to quantify functional complexity even in the absence of fitness data.

Multiferoic oxides have enormous application potential thanks to the mutually coupled magnetic and dielectric response embedded in a standalone material. Among them, the unique case is the cobalt chromite with spin-induced electric polarization locked to the magnetization direction and propagation vector of the spiral magnetic phase. The nature of the ground state magnetic structure gives rise to complex size dependent magnetic behaviour, which collapses when reaching a critical particle size. In our work, we focused on preparation of standalone cobalt chromite nanoparticles (NPs). We introduced hydrothermal decomposition of cobalt(II)/chromium(III) oleates in water/ethanol system without need of additional thermal treatment, which lead to stable cobalt chromite nanoparticles with diameter of 3.0(1)-4.2(1) nm and log normal size distribution of 12-16%. The size at the edge of the critical limit was tuned by the reaction temperature reaching typically 240±10 o C. The as-prepared NPs are coated with covalently bonded oleic acid and can be easily dispersed in non-polar solvents, which makes them excellent candidates for custom surface modifications. The NPs were studied using large number of characterization techniques: powder x-ray diffraction, transmission electron microscopy, small-angle x-ray scattering, and vibrational spectroscopies. The impact of size effect on magnetic properties was also investigated by temperature and magnetic field dependent magnetization, a.c. susceptibility and diffuse neutron scattering. The onset of collective glassy state due to the collapse of long range conical magnetic order was observed. The uniform cobalt chromite NPs coated with oleic acid with size of 3-4 nm are excellent prototypes for studying the size effect on magnetic (and feroic), and can be subjected to manifold surface functionalization required for their embedding in smart nanostructures and nanocomposites.

Experiments featuring non-equilibrium glassy dynamics under temperature changes still await interpretation. There is a widespread feeling that temperature chaos (an extreme sensitivity of the glass to temperature changes) should play a major role but, up to now, this phenomenon has been investigated solely under equilibrium conditions. In fact, the very existence of a chaotic effect in the non-equilibrium dynamics is yet to be established. In this article, we tackle this problem through a large simulation of the 3D Edwards-Anderson model, carried out on the Janus II supercomputer. We find a dynamic effect that closely parallels equilibrium temperature chaos. This dynamic temperature-chaos effect is spatially heterogeneous to a large degree and turns out to be controlled by the spin-glass coherence length ξ. Indeed, an emerging length-scale ξ* rules the crossover from weak (at ξ ≪ ξ*) to strong chaos (ξ ≫ ξ*). Extrapolations of ξ* to relevant experimental conditions are provided.

Significance The Mpemba effect, wherein an initially hotter system relaxes faster when quenched to lower temperatures than an initially cooler system, has attracted much attention. Paradoxically, its very existence is a hot topic. Using massive numerical simulations, we show unambiguously that the Mpemba effect is present in the archetypical model system for complex behavior, spin glasses. We find that the Mpemba effect in spin glasses is due to the aging dynamics of the internal energy, as controlled by the nonequilibrium spin-glass coherence length. Interestingly, the effect is not present when the system remains all of the time in the paramagnetic phase. Therefore, the Mpemba effect suggests itself as an effective probe for a glass transition, potentially useful for other glass-forming systems.

We have performed a very accurate computation of the nonequilibrium fluctuation-dissipation ratio for the 3D 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. Our main result is a quantitative statics-dynamics dictionary, which could allow the experimental exploration of important features of the spin-glass phase without requiring uncontrollable extrapolations to infinite times or system sizes.

In this work, we present a mathematical study of stability and controllability of one-dimensional network of ferromagnetic particles. The control is the magnetic field generated by a dipole whose position and whose amplitude can be selected. The evolution of the magnetic field in the network of particules is described by the Landau-Lifschitz equation. First, we model a network of ellipsoidal shape ferromagnetic particles. Then, we prove the stability of relevant configurations and discuss the controllability by the means of the external magnetic field induced by the magnetic dipole. Finally some numerical results illustrate the stability and the controllability results.

A new protocol of the zero-field-cooled (ZFC) magnetization process is studied experimentally on an Ising spin-glass (SG) Fe0.50Mn0.50TiO3 and numerically on the Edwards-Anderson Ising SG model. Although the time scales differ very much between the experiment and the simulation, the behavior of the ZFC magnetization observed in the two systems can be interpreted by means of a common scaling expression based on the droplet picture. The results strongly suggest that the SG coherence length, or the mean size of droplet excitations, involved even in the experimental ZFC process, is about a hundred lattice distances or less.

The following papers are dedicated to honoring Joel Lebowitz on the occasion of his ninetieth birthday and his retirement as editor-in-chief of the Journal of Statistical Physics (JSP). These contributions are written by a subset of his many friends, co-authors and admirers. JSP was founded in 1969 by Howard Reiss, then a professor of chemistry at UCLA. Following the pioneering example of Lars Onsager, many chemists did research in statistical physics, rather than just in the more traditional field of thermodynamics. In the description of the board of editors of that time one reads: "Professor Joel L. Lebowitz, Statistical Mechanics of equilibrium and nonequilibrium, biomathematics, biophysics"-an impressive range of interests and competences. In 1975, Joel was appointed editor-in-chief of JSP. Browsing through the volumes of this journal produced under Joel's leadership, one observes a substantial change in its scientific orientation. Joel was an active player and catalyser in an area of statistical physics that had emerged in the 60s and was now featuring spectacular progress: rigorous statistical mechanics. Papers published in JSP no longer came out of only physics or chemistry departments but were often written in mathematics departments. Besides statistical mechanics, Joel showed a very lively interest in several other fields, such as deterministic chaos, which then got featured in JSP. As one example, the late Mitchell Feigenbaum's seminal analysis of universality in the period-doubling bifurcations exhibited by families of maps from the unit interval to itself was published in JSP. Joel made use of JSP to announce the programs of his legendary Statistical Mechanics Conferences. The first one to be announced there was number 34. It took place in December 1975 when Joel was still a professor at Yeshiva University. In December of this year the 123rd conference is scheduled to take place. In 1977, Joel moved to Rutgers University, where he holds the prestigious George William Hill Professorship of Mathematics and Physics. The editorial board of JSP has traditionally been rather large, on the order of thirty members. It has been rejuvenated periodically. Its members have been tasked with attracting excellent papers to the journal and assisting in the reviewing of papers submitted for publication. Joel handled every single paper sent to the journal. Years ago, one would see stacks of brownish folders filled with papers considered for publication in JSP on his desk, in his car and at home. Nowadays, such stacks have become virtual-thanks to the 'Editorial Manager'.