Spin Glasses

We have recently shown that BiFeO 3 has at least four different magnetic phases, contrary to the conventional wisdom. Below room temperature it undergoes spin reorientation transitions at T 2 ¼ 200 K and T 1 ¼ 140 K analogous to those in orthoferrites; and above room temperature it undergoes a structural transition near 1851C first reported by Polomska et al. This may help explain the apparent linear magnetoelectric effect at 201C reported by D. Lebeugle et al. [Phys. Rev. Lett. 100, 227602 (2008)] which is nominally forbidden due to the long wavelength cycloidal spin structure assumed. We also find evidence of an unusual acentric spin glass below ca. 200 K, related not to T N but to T 1 and T 2 .

In a pioneering work ,  Mézard and Parisi proved that methods from the theory of disordered systems at low temperature can be used to solve very difficult combinatorial optimisation problems, being possible to assign an energy to their configurations and proceed with the usual apparatus of statistical mechanics. Moreover, numerical simulations showed reach behaviors that, as well as being approachable by replica calculations, opened a lot of interesting questions. Among the variety of problems that one can study in this context this work focused on the linear sum assignment problem, which can be described for example as the assignment of n tasks to n workers in such a way that the total time of execution of the tasks is minimum, being known that worker i spends tij seconds to complete the task j. The work was developed in two stages: first it was constructed and tested a C++ implementation of the Jonker-Volgenant algorithm that solves a general linear sum assignment problem; this code was used to study the Euclidean bipartite matching problem in D dimensions, where frustration is imposed by the geometry of the ambient space, and to see how this problem reaches its mean field approximation in the D → ∞limit (the random assignment problem), where the assignment cost is completely aleatory.

We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of the flipped region. Using a new interpolation method, which extends to the entire circle the standard interpolation technique, we show by integration by parts that the bound imply new overlap identities for the equilibrium state. As a side result the case of the non-interacting random field is analyzed and the triviality of its overlap distribution proved.

All higher-spin (s≥1/2) Ising spin glasses are studied by renormalization-group theory in spatial dimension d=3, exactly on a d=3 hierarchical model and, simultaneously, by the Migdal-Kadanoff approximation on the cubic lattice. The s-sequence of global phase diagrams, the chaos Lyapunov exponent, and the spin-glass runaway exponent are calculated. It is found that, in d=3, a finite-temperature spin-glass phase occurs for all spin values, including the continuum limit of s→∞. The phase diagrams, with increasing spin s, saturate to a limit value. The spin-glass phase, for all s, exhibits chaotic behavior under rescalings, with the calculated Lyapunov exponent of  λ=1.93 and runaway exponent of yR=0.24, showing simultaneous strong-chaos and strong-coupling behavior. The ferromagnetic-spin-glass and spin-glass-antiferromagnetic phase transitions occurring, along their whole length, respectively at pt=0.37 and 0.63 are unaffected by s, confirming the percolative nature of this phase transition.

We report the magnetic characterization of the Cr-doped layered dichalcogenide TiSe 2. The temperature dependent magnetic susceptibilities are typical of those seen in geometrically frustrated insulating antiferromagnets. The Cr moment is close to the spin-only value, and the Curie−Weiss temperatures (θ cw) are between −90 and −230 K. Freezing of the spin system, which is glassy, characterized by peaks in the ac and dc susceptibility and specific heat, does not occur until below T/θ cw = 0.05. The CDW transition seen in the resistivity for pure TiSe 2 is still present for 3% Cr substitution but is absent by 10% substitution, above which the materials are metallic and p-type. Structural refinements, magnetic characterization , and chemical considerations indicate that the materials are of the type Ti 1−x Cr x Se 2‑x/2 for 0 ≤ x ≤ 0.6. ■ INTRODUCTION Frustration of magnetic ordering arises in both atomically disordered systems and systems where the magnetic interactions are not compatible with the underlying structural symmetry. 1−5 Classical spin glasses and systems with magnetic ions on triangular or tetrahedral lattices display such frustration. The most-often-studied materials with strong geometric magnetic frustration are electrically insulating or at best strongly semiconducting, 5−16 and classical spin glass systems can be either metallic or semiconducting. 17 Typically, frustrated magnetic materials are characterized by a Curie−Weiss theta θ cw that is significantly greater than the spin freezing temperature T f. The frustration index f = θ cw /T f is often taken as a general characterization of the degree of frustration. The MX 2 layered transition-metal dichalcogenides (TMDCs, M = Mo, W, V, Nb, Ta, Ti, Zr, Hf, and Re, and X = Se, S, or Te) are a large family of solids with layered triangular metal lattices and have long been of interest due to the rich electronic properties that arise from their low dimensionality (see, e.g. refs 18−22). Within the TMDCs, 1T-TiSe 2 has attracted special attention due to the presence of a Charge Density Wave (CDW) that onsets at 200 K. 22,23 The material has trigonal symmetry, 24 with TiSe 6 octahedra sharing edges in triangular geometry TiSe 2 layers that are bonded to each other by Se−Se van der Waals forces (Figure 1a). Here we study the effect of Cr substitution for Ti in 1T-TiSe 2. We find that as Cr atoms are substituted for Ti, they induce metal occupancy in the van der Waals gap between the TiSe 2 layers (Figure 1a). We interpret our data to indicate that at concentrations less than about 20%, the Cr ions primarily occupy the interstitial octahedral sites in the van der Waals layers, but at higher concentrations they occupy both the octahedral interstitial sites and sites in the Ti layers; when they do that they then displace some Ti into the interstitial positions and the system becomes quite disordered. (The materials system is complex: previous studies 25,26 of Cr-intercalated TiSe 2 yielded magnetic properties that are significantly different from those that are observed here, implying that the magnetic behavior of the system may be dependent on synthetic conditions.) Cr ions most frequently are ionic and have the oxidation state Cr 3+ in solids due to their very strong Hunds-rule coupling. 27 In a material like TiSe 2 , which is a small band gap semiconductor with a conduction band made from empty Ti d states and a valence band made from filled Se p states (i.e., consisting of Ti 4+ and Se 2−), the presence of Cr 3+ along with Ti 4+ and Se 2− requires a decrease in the Se to metal ratio to below 2:1 and a formula Ti 1−x Cr x Se 2‑x/2 to maintain charge neutrality. Our XPS analysis supports these formal oxidation state assignments. This picture for Cr-doped TiSe 2 is further supported by the materials synthesis, the diffraction data, the magnetic data, and the presence of two types of magnetic spins clearly seen in the ac susceptibility for higher x materials. The DC magnetic susceptibilities confirm that the Cr moments in Ti 1−x Cr x Se 2‑x/2 are within experimental error of the expected Cr 3+ spin-only value. 28 The antiferromagnetic Curie−Weiss temperatures are large, between −90 and −230 K. The freezing

The pyrochlore oxide (Ce IV 0.67 Na 0.33) 2 Ru IV 2 O 7 crystallizes directly as a phase-pure sample, without the need for postsynthesis annealing, from aqueous solutions of Ru 3þ , Ce 3þ , and sodium hydroxide in the presence of hydrogen peroxide as oxidizing agent at less than 250°C. The structure has been refined using powder neutron diffraction and is consistent with electron diffraction and EDXA analysis performed using transmission electron microscopy (cubic Fd3m with a = 10.1659(1) Å). The pyrochlore phase is metastable and upon heating to ∼400°C begins to phase separate to ultimately yield a mixture including Na 2 Ru 4 O 9 , RuO 2 , Ce 2 O 3 , and CeO 2. Magnetization measurements confirm that the material is a new example of a B-site magnetic pyrochlore, analogous to the known phase Y 2 Ru 2 O 7 , but that show evidence for magnetic frustration at low temperatures. Heat capacity measurements and low-temperature neutron diffraction indicate the possibility of spin-glass-like behavior with no evidence of long-range magnetic order achieved at low temperature.

We report the bulk magnetic properties of a yet unexplored vanadium-based multi-valenced
spinel system, Zn3V3O8. A Curie–Weiss fit of our dc magnetic susceptibility χ(T ) data
in the temperature region of 140–300K yields a Curie constant C = 0.75 cm3Kmole−1 V−1,
θCW = −370 K. We have observed a splitting between the zero field cooled (ZFC) and
field cooled (FC) susceptibility curves below a temperature Tirr of about 6.3K. The value of
the ‘frustration parameter’ ( |θCW|
TN
∼ 100) suggests that the system is strongly frustrated. From
the ac susceptibility measurements we find a logarithmic variation of freezing temperature (Tf )
with frequency ν attesting to the formation of a spin glass below Tf . However, the value of the
characteristic frequency obtained from the Vogel–Fulcher fit suggests that the ground state is
closer to a cluster glass rather than a conventional spin glass. We explored further consequences
of the spin glass behavior and observed aging phenomena and memory effect (both in ZFC and
FC).We found that a positive temperature cycle erases the memory, as predicted by the hierarchical
model. From the heat capacityCP data, a hump-like anomalywas observed inCP /T at about
3.75 K. Below this temperature the magnetic heat capacity shows a nearly linear dependence
with T which is consistent with the formation of a spin glass state below Tf in Zn3V3O8.

Measurements were made of in-situ X-ray diffraction, electrical resistivity and magnetic susceptibility for a series of newly found ternary alloys CuMPt 6 with M=Ti, V, Cr, Mn, Fe, Co and Ni. They possess, after appropriate heat treatment, the Cu 3 Au-type ordered structure, though the ordering is not complete for M=Ni. They are fairly good electrical conductor with a specific resistivity of around 6 x10-3 ohm ･ m. A general trend has been found in the magnetic property: nonmagnetic-spin-glass-like-ferromagneticparamagnetic, with increasing atomic number of M. The alloy with M=Mn, however, is specific among the seven alloys in that it undergoes secondary ordering into the cubic ABC 6type structure and is regarded as a counterpart of the Heusler alloy forming in the bcc systems.

Research Program Outline: Technophysics: The Formal Study of Smart Networks and Complex System Criticality

The aim of this research program is to formalize research regarding technophysics (the application of physics to the study of technology) and smart networks (intelligent autonomously-operating networks), particularly in the areas of study proposed in this research agenda.

We present a general formalism to make the Replica-Symmetric and Replica-Symmetry-Breaking ansatz in the context of Kikuchi's Cluster Variational Method (CVM). Using replicas and the message-passing formulation of CVM we obtain a variational expression of the replicated free energy of a system with quenched disorder, both averaged and on a single sample, and make the hierarchical ansatz using functionals of functions of fields to represent the messages. We obtain a set of integral equations for the message functionals. The main difference with the Bethe case is that the functionals appear in the equations in implicit form and are not positive definite, thus standard iterative population dynamic algorithms cannot be used to determine them. In the simplest cases the solution could be obtained iteratively using Fourier transforms.

This paper develops the theory of affine Euler-Poincaré and affine Lie-Poisson reductions and applies these processes to various examples of complex fluids, including Yang-Mills and Hall magnetohydrodynamics for fluids and superfluids, spin glasses, microfluids, and liquid crystals. As a consequence of the Lagrangian approach, the variational formulation of the equations is determined. On the Hamiltonian side, the associated Poisson brackets are obtained by reduction of a canonical cotangent bundle. A Kelvin-Noether circulation theorem is presented and is applied to these examples.

In this work we introduce and analyze the stochastic dynamics obeyed by a model of an immune network recently introduced by the authors. We develop Fokker-Planck equations for the single lymphocyte behavior and coarse grained Langevin schemes for the averaged clone behavior. After showing agreement with real systems (as a short path Jerne cascade), we suggest, both with analytical and numerical arguments, explanations for the generation of (metastable) memory cells, improvement of the secondary response (both in the quality and quantity) and bell shaped modulation against infections as a natural behavior. The whole emerges from the model without being postulated a-priori as it often occurs in second generation immune networks: so the aim of the work is to present some out-ofequilibrium features of this model and to highlight mechanisms which can replace a-priori assumptions in view of further detailed analysis in theoretical systemic immunology.

We propose an efficient Monte Carlo algorithm for simulating a "hardlyrelaxing" system, in which many replicas with different temperatures are simultaneously simulated and a virtual process exchanging configurations of these replica is introduced. This exchange process is expected to let the system at low temperatures escape from a local minimum. By using this algorithm the three-dimensional ±J Ising spin glass model is studied. The ergodicity time in this method is found much smaller than that of the multicanonical method. In particular the time correlation function almost follows an exponential decay whose relaxation time is comparable to the ergodicity time at low temperatures. It suggests that the system relaxes very rapidly through the exchange process even in the low temperature phase.

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda–Guerra relations determines the distribution of overlaps among...

By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here we extend this argument in order to compare the limiting free energy with the expression given by the Parisi Ansatz, and including full spontaneous replica symmetry breaking. Our main result is that the quenched average of the free energy is bounded from below by the value given in the Parisi Ansatz, uniformly in the size of the system. Moreover, the difference between the two expressions is given in the form of a sum rule, extending our previous work on the comparison between the true free energy and its replica symmetric Sherrington-Kirkpatrick approximation. We give also a variational bound for the infinite volume limit of the ground state energy per site.

Magnetic phase transitions in the rare-earth intermetallic compound Nd 5Ge 3 have been investigated using a single crystal. Magnetic measurements confirm that Nd 5Ge 3 is in the antiferromagentic state below TN=51 K, in literature. An irreversible magnetic-field-induced antiferromagentic to ferromagnetic transition has been found below Tt=26 K. In this state, a metamagnetic transition takes place in the first magnetizing process; a ferromagnetic state having a remanent magnetization MR is stabilized after removing the external magnetic field. MR does not show noticeable relaxation behavior and a rectangular-type hysteresis loop is maintained in the following magnetization process. As origin of the irreversibility, a martensitic structural phase transition under the external field can be considered. The magnetic-field cooling effect on the magnetic susceptibility indicates the coexistence of a kind of spin-glass state with long-range antiferromagnetic ordering.

We present a mean-field study of the magnetic phase diagram of
Ni1-xMox and
Ni1-xWx alloys. The pair energies that enter
the internal energy part of the free energy are obtained from a
first-principles calculation. We try to understand why spin-glass phase
is not observed in these alloys.

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the overlaps among s replicas. Add one replica s + 1. Then, the overlap q a,s+1 between one of the first s replicas, let us say a, and the added s + 1 is either independent of the former ones, or it is identical to one of the overlaps q ab , with b running among the first s replicas, excluding a. Each of these cases has equal probability 1/s.

The spin-glass phase in the LiHo x Y 1−x F 4 compound is considered. At zero transverse field this system is well described by the classical Ising model. At finite transverse field deviations from the transverse field quantum Ising model are significant, and one must take properly into account the hyperfine interactions, the off-diagonal terms in the dipolar interactions, and details of the full J = 8 spin Hamiltonian to obtain the correct physical picture. In particular, the system is not a spin glass at finite transverse fields and does not show quantum criticality.

Unusual positive exchange bias found in Fe/CoOx nanoparticle bilayer films is correlated to a characteristic magnetic spin-glass (SG) in CoOx, with the SG magnetization coupled antiparallel with the Fe magnetization upon field cooling. This SG magnetization has strong field- and time-dependence which displays unusual upward magnetic relaxation behavior in thermoremanent magnetization measurements. The antiparallel coupling is shown to result predominantly from the antiferromagnetic superexchange of the Fe2+-O-Co3+ couple, of the oxygen-terminated CoOx at the interface. These experimental results reveal the possibility of manipulating the exchange bias effect via an indirect exchange coupling mechanism.

We propose the binding information as an information theoretic measure of complexity between multiple random variables, such as those found in the Ising or Potts models of interacting spins, and compare it with several previously proposed measures of statistical complexity, including excess entropy, Bialek et al 's predictive information, and the multi-information. We discuss and prove some of the properties of binding information, particularly in relation to multi-information and entropy, and show that, in the case of binary random variables interactions, the processes which maximise binding information are the 'parity' processes. The computation of binding information is demonstrated on Ising models of finite spin systems, showing that various upper and lower bounds are respected and also that there is a strong relationship between the introduction of high-order interactions and an increase of binding-information. Finally we discuss some of the implications this has for the use of the binding information as a measure of complexity.

We prove, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type (Edwards-Anderson) spin-glass system. Using the properties of CNN we show that one single operation (template) always yields a local minimum of the spin-glass energy function. This way a very fast optimization method, similar to simulated annealing, can be built. Estimating the simulation time needed with our optimization algorithm on CNN based computers, and comparing it with the time needed on normal digital computers using the simulated annealing algorithm, the results are astonishing: CNN computers could be faster than digital computers already at 10times10 lattice sizes. The local control of the template parameters was already partially realized on some of the hardwares, we think this study could further motivate their development in this direction.

With the aim of describing a general benchmark for several complex systems, we analyze, by means of statistical mechanics, a sparse network with random competitive interactions among dichotomic variables pasted on the nodes. The model is described by an infinite series of order parameters (the multioverlaps) and has two tunable degrees of freedom: the noise level and the connectivity (the averaged number of links). We show that there are no multiple transition lines, one for every order parameter, as a naive approach would suggest, but just one corresponding to ergodicity breaking. We explain this scenario within a novel and simple mathematical technique via a driving mechanism such that, as the first order parameter (the two replica overlap) becomes different from zero due to a real second order phase transition (with properly associated diverging rescaled fluctuations), it enforces all the other multi-overlaps toward positive values thanks to the strong correlations which develop among themselves and the two replica overlap at the critical line.

The temperature (T )-shift protcol of aging in the 3 dimensional (3D) Edwards-Anderson (EA) spin-glass (SG) model is studied through the out-of-phase component of the ac susceptibility simulated by the Monte Carlo method. For processes with a small magnitude of the T -shift, ∆T , the memory imprinted before the T -shift is preserved under the T -change and the SG short-range order continuously grows after the T -shift, which we call the cumulative memory scenario. For a negative T -shift process with a large ∆T the deviation from the cumulative memory scenario has been observed for the first time in the numerical simulation. We attribute the phenomenon to the 'chaos effect' which, we argue, is qualitatively different from the so-called rejuvenation effect observed just after the T -shift.

The presence of macroscopic phase separation into superconducting and spin-glass-like magnetic phases in LaFeAs(O 1−x F x) is demonstrated by muon spin rotation measurement in a sample near the phase boundary (x = 0.06). Both magnetism and superconductivity develop simultaneously below a common critical temperature, T m ≃ T c ≃ 18 K. This remarkable accordance strongly suggests that the electronic correlations leading to these two competing ground states share a common origin.

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 hierarc...

Polycrystalline SrRu 1−x Mn x O 3 (0 x 1) perovskite oxides have been prepared by a conventional solid-state reaction technique. Magnetic and magnetotransport properties are measured using a superconducting quantum interference device (SQUID, Quantum Design MPMS) over a temperature range of 4-300 K. The substitution of Mn ions for Ru drives the system from a ferromagnetic state, SrRuO 3 , to an antiferromagnetic state, SrMnO 3 , which is basically similar to observations in single-crystal SrRu 1−x Mn x O 3 (Cao et al 2005 Phys. Rev. B 71 035104). However, the measurement of dc magnetization and ac susceptibility indicates that magnetic phase transition with x is more complicated and pronounced than those in single crystals. The phase transition process as temperature is reduced covers paramagnetism-antiferromagnetism (PM-AFM), paramagnetism-ferromagnetism (PM-FM) and ferromagnetismcluster glass-spin glass (FM/CG/SG) etc. In particular, we observe a large lowtemperature magnetoresistance (MR) of −41% for the sample x = 0.55, which is the largest MR measured in Mn-doped SrRuO 3. The experiment has verified that the large MR stems predominantly from a unique spin glass state in the polycrystalline alloy. These results substantiate that Ru-based oxides doped with 3d/4d transition metals have the potential for use in spintronics devices due to their adjustable phase transition, depending upon the level and nature of 3d/4d ion doping.

The mean field spin glass model is analyzed by a combination of mathematically rigororous methods and a powerful Ansatz. The method exploited is general, and can be applied to others disordered mean field models such as, e.g., neural networks. It is well known that the probability measure of overlaps among replicas carries the whole physical content of these models. A functional order parameter of Parisi type is introduced by rigorous methods, according to previous works by F. Guerra. By the Ansatz that the functional order parameter is the correct order parameter of the model, we explicitly find the full overlap distribution. The physical interpretation of the functional order parameter is obtained, and ultrametricity of overlaps is derived as a natural consequence of a branching diffusion process. It is shown by explicit construction that ultrametricity of the 3-replicas overlap distribution together with the Ghirlanda-Guerra relations determines the distribution of overlaps among s replicas, for any s, in terms of the one-overlap distribution.

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.

Our measured dielectric constant and mechanical response of multiferroic BiFeO 3 indicate four phase transitions below room temperature. Features correlate with those reported at 50 K (from a peak in the zero-field-cooled magnetic susceptibility) and 230 K (from splitting between field-cooled and zero-field-cooled magnetic data; Singh et al 2008 Phys. Rev. B 77 144403), and those at 140 and 200 K (from the magnon light scattering cross section; Singh et al 2008 J.

Elastic and inelastic neutron scattering (ENS and INS) experiments were performed on a single crystal of
(Ni0.4Mn0.6)TiO3 (NMTO) to study the spatial correlations and dynamics of spins in the XY-like spin-glass (SG)
state. Magnetization measurements reveal signatures of SG behavior in NMTO with a freezing temperature of
TSG ∼ 9.1K. The ENS experiments indicate that the intensity of magnetic diffuse scattering starts to increase
around 12 K, which is close to TSG. Also, spin-spin correlation lengths (ξ ) at 1.5 K are approximately (21 ± 1) and
(73 ± 2) °A in the interlayer and the in-plane directions, respectively, demonstrating that magnetic correlations in
NMTO exhibit quasi-two-dimensional antiferromagnetic order. In addition, critical exponent (β) is determined
to be 0.37 ± 0.02 from the intensity of magnetic diffuse scattering confirms the XY-like SG state of NMTO. INS
results show quasielastic neutron scattering (QENS) profiles below TSG. The lifetime of dynamic correlations τ ∼
/L, obtained from the half-width at half-maximum of the Lorentzian (L) QENS profiles, are approximately
(16 ± 1) and (16 ± 2) ps at 10Kfor two positions (0.00, 0.00, 1.52) and (0.01, 0.01, 1.50), respectively. Therefore,
our experimental findings demonstrate that short-range-ordered antiferromagnetic clusters with short-lived spin
correlations are present in the XY-like SG state of NMTO.

We study the 3d Ising spin glass with ±1 couplings. We introduce a modified local action. We use finite size scaling techniques and very large lattice simulations. We find that our data are compatible both with a finite T transition and with a T = 0 singularity of an unusual type.

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. r

Measurements were made of in situ X-ray diffraction, electrical resistivity, and magnetic susceptibility for a series of newly found ternary alloys CuMPt 6 with M = Ti, V, Cr, Mn, Fe, Co, and Ni. They possess, after appropriate heat treatment, the Cu 3 Au-type ordered structure, though the ordering is not complete for M = Ni. They are fairly good electrical conductor with a specific resistivity of around 6 × 10 -3 ohm m. A general trend has been found in the magnetic property: nonmagnetic-spin-glass-like-ferromagnetic-paramagnetic, with increasing atomic number of M.

We study the behavior of the fully connected Ising spin glass in a transverse field G at T ¼ 0 by exact diagonalization techniques. We find that the order parameter grows linearly with G c À G below G c : The exact diagonalization method shows a rather good scaling behavior to the large system limit. r

An outstanding open problem is whether collective social phenomena occurring over short timescales can systematically reduce cultural heterogeneity in the long run, and whether offline and online human interactions contribute differently to the process. Theoretical models suggest that short-term collective behavior and longterm cultural diversity are mutually excluding, since they require very different levels of social influence. The latter jointly depends on two factors: the topology of the underlying social network and the overlap between individuals in multidimensional cultural space. However, while the empirical properties of social networks are intensively studied, little is known about the large-scale organization of real societies in cultural space, so that random input specifications are necessarily used in models. Here we use a large dataset to perform a high-dimensional analysis of the scientific beliefs of thousands of Europeans. We find that interopinion correlations determine a nontrivial ultrametric hierarchy of individuals in cultural space. When empirical data are used as inputs in models, ultrametricity has strong and counterintuitive effects. On short timescales, it facilitates a symmetry-breaking phase transition triggering coordinated social behavior. On long timescales, it suppresses cultural convergence by restricting it within disjoint groups. Moreover, ultrametricity implies that these results are surprisingly robust to modifications of the dynamical rules considered. Thus the empirical distribution of individuals in cultural space appears to systematically optimize the coexistence of short-term collective behavior and long-term cultural diversity, which can be realized simultaneously for the same moderate level of mutual influence in a diverse range of online and offline settings.

We study the problem of determining the Hamiltonian of a fully connected Ising Spin Glass of N units from a set of measurements, whose sizes needs to be O(N 2) bits. The student-teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with arbitrary couplings. The set of measurements consists of data about the local minima of the rugged energy landscape. We compare simulations and analytical approximations for the resulting learning curves obtained by using different algorithms.

An analysis of Mn substitution in SrTiO 3 is performed in order to understand the origin of reported spin coupling in lightly Mn-doped SrTiO 3. The spin glass state magnetoelectrically coupled to the dipolar glass state has previously been reported for SrTiO 3 substituted with only 2% of Mn on the B-site. An analysis of the substitution mechanism for A-and B-site doping shows a strong infl uence of processing conditions, such as processing temperature, oxygen partial pressure, and off-stoichiometry. The required conditions for a site-selective substitution are defi ned, which yield a single-phase and almost defect-free perovskite. Magnetic measurements show no magnetic anomalies resulting from spin coupling and only a simple paramagnetic behavior. Magnetic anomalies are observed only for the samples in which Mn is misplaced within the cation sublattice of the SrTiO 3 perovskite. This occurs due to improper material processing, which causes initially unpredicted changes in the valence state of the Mn and results in the formation of structural defects and irregularities associated with segregation and nucleation of the magnetic species. Previously reported spin coupling in Mn-doped SrTiO 3 is not an intrinsic phenomenon and cannot be treated as a spin glass.

We study the problem of determining the Hamiltonian of a fully connected Ising spin glass of N units from a set of measurements, whose sizes needs to be O(N2) bits. The student–teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with arbitrary couplings. The set of measurements consists of data about the local minima of the rugged energy landscape. We compare simulations and analytical approximations for the resulting learning curves obtained by using different algorithms.

Let X ⊂ A Z d be a 2-dimensional subshift of finite type. We prove that any 2-dimensional subshift of finite type can be characterized by a square matrix of infinite dimension. We extend our result to a general d-dimensional case. We prove that the multidimensional shift space is non-empty if and only if the matrix obtained is of positive dimension. In the process, we give an alternative view of the necessary and sufficient conditions obtained for the non-emptiness of the multidimensional shift space. We also give sufficient conditions for the shift space X to exhibit periodic points.