Spin Glasses

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.

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.

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.

We study point processes on the real line whose configurations X are locally finite, have a maximum and evolve through increments which are functions of correlated Gaussian variables. The correlations are intrinsic to the points and quantified by a matrix Q = {q ij } i,j ∈N. A probability measure on the pair (X, Q) is said to be quasi-stationary if the joint law of the gaps of X and of Q is invariant under the evolution. A known class of universally quasi-stationary processes is given by the Ruelle Probability Cascades (RPC), which are based on hierarchically nested Poisson-Dirichlet processes. It was conjectured that up to some natural superpositions these processes exhausted the class of laws which are robustly quasi-stationary. The main result of this work is a proof of this conjecture for the case where q ij assume only a finite number of values. The result is of relevance for mean-field spin glass models, where the evolution corresponds to the cavity dynamics, and where the hierarchical organization of the Gibbs measure was first proposed as an ansatz.

We present a theoretical study of ordering in Fe-Al alloys assuming different underlying magnetic structures: paramagnetic, ferromagnetic, and disordered local moments ͑DLM's͒. We calculate the effective pair ͑chemical͒ interactions using the generalized perturbation method ͑GPM͒ in the linear muffin tin orbital basis. The reference medium for the GPM is chosen as the completely disordered state of the alloy, with its electronic structure described via the coherent potential approximation. The effective pair interactions are used to obtain the ordered superlattice structures and to estimate the order-disorder transition temperatures. The tendency of primary ordering to the B2 structure and secondary ordering to the DO 3 structure is examined as a function of Fe concentration. We find that the tendency to B2 ͑CsCl͒ ordering decreases in sequence from the paramagnetic to the DLM's and to the ferromagnetic model. The tendency to secondary ordering in the DO 3 structure is strongest in the ferromagnetic model and is found to increase with Fe concentration due to enhanced spin polarization. Factors such as lattice relaxation, charge transfer, and alloy volume ͑per atom͒ are found to be much more important for secondary than for primary ordering. Although the model provides a way to study the ordering tendency in the alloy based on an ab initio electronic structure calculation, it is deficient in capturing all the intricacies of the interplay between magnetic and chemical structure. Effects of spin fluctuations on the order-disorder transition are also neglected. ͓S0163-1829͑97͒03413-9͔

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.

Co/Pt multilayers can exhibit considerable exchange bias along the film normal when grown onto or covered by an antiferromagnetic IrMn layer. The magnitude of the bias effect depends strongly on the selection of the buffer layers and is largest for Co/Pt multilayers with small perpendicular anisotropy. This counterintuitive result is explained by opposite dependencies of exchange bias and magnetic anisotropy on the degree of film texture and grain size. Interface roughness also influences the perpendicular exchange bias field. The largest biases are measured on smooth films. Interlayer mixing during post-deposition annealing procedures decreases the exchange bias field of IrMn-capped Co/Pt multilayers.

The time decay of the thermoremanent magnetization(TRM) of the Fe 80−x Ni x Cr 20 (14 ≤ x ≤ 30) alloys has been measured for four different magnetic phases within the fcc γ-phase using a SQUID magnetometer. In the spin-glass phase(SG)(X=19) very distinct ageing effects are observed where M(t) can be described as M (t) = M 0 (t/t w) −γ exp[−(t/τ) 1−n ] for the entire time domain. In the reentrant spin-glass(RSG)(X= 23 and 26), M(t) can be better represented by the stretched exponential with an addition of a constant term which can be well explained by the Gabay-Toulouse(GT) model. We have also measured the linear and non-linear ac susceptibilities for the sample X=23 and confirmed the presence of the ferromagnetic(FM) ordering down to the lowest temperature. In the RSG(X=23), the TRM shows a minimum near T c and a local maximum just above T c. In the FM phase (X=30) the popular prediction of the power law decay of the TRM is observed. The latter is indistinguishable from the stretched exponential in the antiferromagnetic(AF) phase (X=14).

DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:

The consequences of rotational-symmetry breaking in Heisenberg spin-glasses are studied with use of order parameters which are time-dependent SO(3) rotation matrices. A microscopic derivation of the hydrodynamic "triad" theory, including the effect of small magnetic fields and random anisotropies, is presented. In the mean-field limit the finitetime exchange stiffness and macroscopic anisotropy constants vanish near the transition temperature T~a s (T~-T}",p, = 3.

Square lattices with Ising spins at the sites and AEJ exchange interactions between nearest neighbors are one of the realizations of the Edwards-Anderson model originally proposed to mimic spin glasses. Such systems produce a complex configuration space due to frustration originated in local competing fields. Reaching exact results for physical parameters is limited to the ground states of small systems. Due to this complexity it is unavoidable to use numerical methods subject to controlled error to attempt a good approximation for large enough systems. Here we make use of the thermodynamic integration method to obtain energy and remnant entropy for lattices 20 Â 20 with variable concentration x of ferromagnetic bonds. It turns out that both energy and entropy reach their minima at x ¼ 0:0 and 1.0 growing towards the symmetric point x ¼ 0:5 in a similar way, leading to an almost linear relationship between entropy and energy.

In this topical review we discuss the nature of the low-temperature phase in both infiniteranged and short-ranged spin glasses. We analyze the meaning of pure states in spin glasses, and distinguish between physical, or "observable", states and (probably) unphysical, "invisible" states. We review replica symmetry breaking, and describe what it would mean in shortranged spin glasses. We introduce the notion of thermodynamic chaos, which leads to the metastate construct. We apply these tools to short-ranged spin glasses, and conclude that replica symmetry breaking, in any form, cannot describe the low-temperature spin glass phase in any finite dimension. We then discuss the remaining possible scenarios that could describe the low-temperature phase, and the differences they exhibit in some of their physical properties-in particular, the interfaces that separate them. We also present rigorous results on metastable states and discuss their connection to thermodynamic states. Finally, we discuss some of the differences between the statistical mechanics of homogeneous systems and those with quenched disorder and frustration.

We report on the magnetic properties of Fe 1−x Al x alloys ͑0.2ഛ x ഛ 0.4͒ produced by mechanical alloying by milling pure element powders for t = 12, 24, and 36 h. The alloys present a bcc lattice with compositional disorder and are ferromagnetic at room temperature, independently of the milling time. The lattice parameter of the x = 0.2 sample presents a small decrease with t, whereas those of the x = 0.3 and 0.4 samples remain constant independently of the milling time. The magnetic properties of the alloys with x = 0.2 and 0.3 do not show important variations with t, while those of x = 0.4 are strongly dependent on the milling time. For this latter alloy it was found that: ͑i͒ despite being the most diluted of the series, it presents a well developed ferromagnetic order at room temperature as the Mössbauer and hysteretic data have shown; ͑ii͒ the temperature dependence of the ac susceptibility and the Mössbauer spectra recorded at different temperatures evidence the occurrence of reentrant spin-glass and superparamagnetic phenomena. The enhancement of the ferromagnetic behavior and the presence of reentrant spin-glass freezing temperature and of a superparamagnetic blocking process are interpreted in terms of a simple localized model based on the disorder present in that alloy and on the occurrence of competitive interactions, namely, the ferromagnetic nearest-neighbor Fe-Fe interactions and the antiferromagnetic near-nearest-neighbor Fe-Fe ones. Taken together, these results evidence that the stabilization of the magnetic order takes place in the x = 0.4 sample exclusively through the induction of compositional disorder and without any contribution from the lattice expansion.

We study, near T" the stability of Parisi's solution for the long-range spin-glass. In addition to the discrete, "longitudinal" spectrum found by Thouless, de Almeida, and Kosterlitz, we find "transverse" bands depending on one or two continuous parameters, and a host of zero modes occupying most of the parameter space. All eigenvalues are non-negative, proving that Parisi's solution is marginally stable.

The cluster variation method has been developed into a general theoretical framework for treating short-range correlations in many-body systems after it was first proposed by Kikuchi in 1951. On the numerical side, a message-passing approach called generalized belief propagation (GBP) was proposed by Yedidia, Freeman and Weiss about a decade ago as a way of computing the minimal value of the cluster variational free energy and the marginal distributions of clusters of variables. However the GBP equations are often redundant, and it is quite a non-trivial task to make the GBP iteration converges to a fixed point. These drawbacks hinder the application of the GBP approach to finite-dimensional frustrated and disordered systems. In this work we report an alternative and simple derivation of the GBP equations starting from the partition function. Based on this derivation we propose a natural and systematic way of removing the redundance of the GBP equations. We apply the simplified generalized belief propagation (SGBP) equations to the two-dimensional and the three-dimensional ferromagnetic Ising model and Edwards-Anderson spin glass model. The numerical results confirm that the SGBP message-passing approach is able to achieve satisfactory performance on these model systems. We also suggest that a subset of the SGBP equations can be neglected in the numerical iteration process without affecting the final results.

This note is concerned with a diluted version of the perceptron model. We establish a replica symmetric formula at high temperature, which is achieved by studying the asymptotic behavior of a given spin magnetization. Our main task will be to identify the order parameter of the system.

Thepreparation andproperties of NbjO, coatings made bythesol-gel process were investigated. Thefilms were deposited byspincoating on In203:Snlglass and quartz substrates from a polymeric solutions of niobia derived from niobium ethoxide. The films were characterized byinvestigation ofthestoichiometry.refractive index, optical transmission, electrochemical behavior. andthemicrostructure. X-ray diffraction studies showed the films to be amorphous forheat treatments below 450°C. X-ray photoelectron spectroscopy (XPS) measurement revealed theO:Nbatomic stoichiometry tobe5:2. Cyclic voltammetric measurements showed thattheNb 20S / 1M LiClOcpropylene carbonate system exhibits electrochemical reversibility beyond I 200 cycles without change in performance. In situ UV-Vis-NIR spectroelectrochemical measurement revealed that Nb 2 0 s films exhibit an electrochromic effect in the spectral range 300<A<2100 nm and remain unchanged in the infrared spectral range. The change in visible transmittance was 40% for a 250nm thick electrode. XPS spectra indicate thatNb(V) is reduced to a lower valence state Nb(IV) in a colored state with injected Li ". The bronze coloration is due to a simultaneous injection of electrons and Li + ions into Nb 20S ' The sol-gel-deposited Nb 20S films are useful for cathodically coloring electrochromic electrodes in electrochromic devices.

We report on a systematic study of the structural, magnetic, and transport properties of high-purity 1T-VS 2 powder samples prepared under high pressure. The results differ notably from those previously obtained by deintercalating Li from LiVS 2. First, no charge-density wave (CDW) is found by transmission electron microscopy down to 94 K, though ab initio phonon calculations unveil a latent CDW instability driven by an acoustic phonon softening at the wave vector q CDW ≈ (0.21,0.21,0) previously reported in deintercalated samples. A further indication of latent lattice instability is given by an anomalous expansion of the V-S bond distance at low temperature. Second, infrared optical absorption and electrical resistivity measurements give evidence of nonmetallic properties, consistent with the observation of no CDW phase. On the other hand, magnetic susceptibility and NMR data suggest the coexistence of localized moments with metallic carriers, in agreement with ab initio band structure calculations. This discrepancy is reconciled by a picture of electron localization induced by disorder or electronic correlations leading to a phase separation of metallic and nonmetallic domains in the nm scale. We conclude that 1T-VS 2 is at the verge of a CDW transition and suggest that residual electronic doping in Li deintercalated samples stabilizes a uniform CDW phase with metallic properties.

In this paper (part XXVI), we analyze some differential equations and integrals concerning Black Hole Physics. We obtain new possible mathematical connections with some sectors of Number Theory, Ramanujan Recurring Numbers, DN Constant and String Theory

A spin-glass system with a smooth or fractal outer surface is studied by renormalization-group theory, in bulk spatial dimension d=3. Independently varying the surface and bulk random-interaction strengths, phase diagrams are calculated. The smooth surface does not have spin-glass ordering in the absence of bulk spin-glass ordering and always has spin-glass ordering when the bulk is spin-glass ordered. With fractal (d>2) surfaces, a sponge is obtained and has surface spin-glass ordering also in the absence of bulk spin-glass ordering. The phase diagram has the only-surface-spin-glass ordered phase, the bulk and surface spin-glass ordered phase, and the disordered phase, and a special multicritical point where these three phases meet. All spin-glass phases have distinct chaotic renormalization-group trajectories, with distinct Lyapunov and runaway exponents which we have calculated.

The infinite-range-interaction Ising spin glass is considered in the presence of an external random magnetic field following a trimodal (three-peak) distribution. Such a distribution corresponds to a bimodal added to a probability p 0 for a field dilution, in such a way that at each site the field h i obeys P (h i) = p + δ(h i −h 0)+p 0 δ(h i)+p − δ(h i +h 0). The model is studied through the replica method and phase diagrams are obtained within the replicasymmetry approximation. It is shown that the border of the ferromagnetic phase may present, for conveniently chosen values of p 0 and h 0 , first-order phase transitions, as well as tricritical points at finite temperatures. Analogous to what happens for the Ising ferromagnet under a trimodal random field, it is verified that the first-order phase transitions are directly related to the dilution in the fields: the extensions of these transitions are reduced for increasing values of p 0. Whenever the delta function at the origin becomes comparable to those at h i = ±h 0 , first-order phase transitions disappear; in fact, the threshold value p * 0 , above which all phase transitions are continuous, is calculated analytically as p * 0 = 2(e 3/2 + 2) −1 ≈ 0.30856. The ferromagnetic boundary at zero temperature also exhibits an interesting behavior: for 0 < p 0 < p * 0 , a single tricritical point occurs, whereas if p 0 > p * 0 the critical frontier is completely continuous; however, for p 0 = p * 0 , a fourthorder critical point appears. The stability analysis of the replica-symmetric solution is performed and the regions of validity of such a solution are identified; in particular, the Almeida-Thouless line in the plane field versus temperature is shown to depend on the weight p 0 .