Signal-to-noise analysis of Hopfield neural networks with a formulation of the dynamics in terms of transition probabilities

We study Hopfield neural networks with infinite connectivity using signal-to-noise analysis with a formulation of the dynamics in terms of transition probabilities. We focus our study on models where the strongest effects of the feedback correlations appear. We introduce an analysis of the path probability of one neuron in order to obtain the contribution of all feedback correlations to the dynamics of this neuron. In this way, we obtain a complete theory for dynamics with order parameter equations identical to those obtained with general functional analysis for finite temperature. In the first part of this work, we present our method in the fully connected Little-Hopfield neural network. We obtain, in a simple and direct way, the order parameter equations found by general functional analysis. In the second part, the exposed method is applied to the fully connected Ashkin-Teller neural network. It is shown that the retrieval quality is improved by introducing four-spin couplings. Simulation results support our theoretical predictions.     

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.     

Chiral spin pairing in helical magnets

A concept of chiral spin pairing is introduced to describe a vector-chiral liquid-crystal order in frustrated spin systems. It is found that the chiral spin pairing is induced by the coupling to phonons through the Dzyaloshinskii-Moriya interaction and the four-spin exchange interaction of the Coulomb origin under the edge-sharing network of magnetic and ligand ions. This produces two successive second-order phase transitions upon cooling: an O(2) chiral spin nematic, i.e., spin cholesteric, order appears with an either parity, and then the O(2) symmetry is broken to yield a helical magnetic order. Possible candidate materials are also discussed as new multiferroic systems.     

Predissociation resonances in CO and IBr. Smooth exterior scaling combined with the discrete variable representation

Smooth exterior scaling (SES) and the discrete variable representation (DVR) are combined to accurately compute predissociation resonances of a bound state non-adiabatically coupled to a dissociative state. For the CO( predissociation interaction good agreement is found with approaches based on optical potentials and complex scaling. The comparison is done both in the diabatic and the adiabatic representation. The effect of the coupling strength in the IBr predissociation interaction and the transition from the diabatic to the adiabatic picture was studied by computing resonances for coupling strengths from up to . The transition from weak (diabatic) to strong (adiabatic) coupling was clearly seen. The intermediate case leads to a complicated resonance distribution. Comparison was made with recent studies using pump-probe spectroscopy [M. Shapiro, M.J.J. Vrakking, A. Stolow, J. Chem. Phys. 110, 2465 (1999)]. It was found that the overall features of the experiment could be explained from the resonance distribution, but for a detailed comparison more accurate potential energy surfaces and couplings are needed. Received 12 July 1999 and Received in final form 6 December 1999     

高分辨核磁共振谱计算机解析方法

本文应用哈密顿矩阵范数逼近方法,利用计算机计算了三自旋、四自旋系统高分辨核磁共振谱的化学位移和偶合常数。与一般迭代程序相比,简化了计算过程,提高了计算精度,并保证了解的唯一性。选择实验能级值作为哈密顿矩阵零级近似,避免了选取初始δ,J值的麻烦。本方法在图谱定量分析中取得了较好效果。     

Magnetic interactions in the monoclinic ludwigite Cu FeO BO

The system Cu₂FeO₂BO₃ is an oxyborate belonging to the family of the ludwigites. In this paper we present AC susceptibility, magnetization measurements and M?ssbauer spectroscopy on this material which allows for a complete characterization of its complex magnetic behavior. We find an hierarchy of interactions which clearly defines three regimes with decreasing temperature. These are associated with, the freezing of the Fe moments, the antiferromagnetic ordering of the Cu sub-lattice and finally the coupling between both systems. Received 25 September 1998     

Magnetic resonance in oxygen-doped La2NiO_{4 + \delta }

We report an investigation of magnetic resonance by ESR in oxygen-doped La₂NiO emphasizing extensively for the first time the role of oxygen stoichiometry. The work is performed at room temperature and on powders with . At low field an hysteresis is detected between increasing and decreasing fields, it depends upon . The resonance lines have characteristic features of ferromagnetic resonance. The intensity () is used as an experimental parameter for investigating the effect of . It allows to built a diagram closely connected to the phase diagram . It suggests a ferromagnetic coupling depending upon . When the (average) structure is tetragonal the low intensity is due to a magnetic polaron of low resistivity. In ranges where a phase separation is detected, the ferromagnetic coupling has a structural origin (DM or local anisotropy) with apparently a strong influence on the electrical resistivity. Received: 3 November 1997 / Accepted: 23 December 1997     

Mixed spin Ising model with four-spin interaction and random crystal field

The effects of fluctuations of the crystal field on the phase diagram of the mixed spin-1/2 and spin-1 Ising model with four-spin interactions are investigated within the finite cluster approximation based on a single-site cluster theory. The state equations are derived for the two-dimensional square lattice. It has been found that the system exhibits a variety of interesting features resulting from the fluctuation of the crystal field interactions. In particular, for low mean value D of the crystal field, the critical temperature is not very sensitive to fluctuations and all transitions are of second order for any value of the four-spin interactions. But for relatively high D, the transition temperature depends on the fluctuation of the crystal field, and the system undergoes tricritical behaviour for any strength of the four-spin interactions. We have also found that the model may exhibit reentrance for appropriate values of the system parameters.     

Melting of a Wigner crystal in an ionic dielectric

The melting of a Wigner Crystal of electrons placed into a host polar material is examined as a function of the density and the temperature. When the coupling to the longitudinal optical modes of the host medium is turned on, the WC is progressively transformed into a polaronic Wigner crystal. We estimate the critical density for crystal melting at zero temperature using the Lindeman criterion. We show that above a certain critical value of the Fr?hlich electron-phonon coupling, the melting towards a quantum liquid of polarons is not possible, and the insulator-to-metal transition is driven by the ionization of the polarons (polaron dissociation). The phase diagram at finite temperature is obtained by making use of the same Lindeman criterion. Results are also provided in the case of an anisotropic electron band mass, showing that the scenario of polaron dissociation can be relevant in anisotropic compounds such as the superconducting cuprates at rather moderate e-ph couplings. Received 13 August 1999     

Mode-coupling crossover in viscous toluene revealed by neutron and light scattering

The dynamics of supercooled toluene, studied in a GHz-THz range by incoherent neutron and depolarized light scattering, is found to be in full accord with mode coupling predictions. Around the susceptibility minimum, neutron spectra are wavenumber independent and proportional to light scattering data; the fast -relaxation scaling law applies; amplitude and frequency diverge with power laws that extrapolate towards a crossover temperature K. Received: 20 June 1997 / Accepted: 3 November 1997     

Perturbation calculation for the eight-vertex model around the Ising point for T → Tc−

The dispersion expansion for the two-point electric correlation function in the eight-vertex model is calculated to first order in the four-spin coupling in the scaling limit. The dispersion expansion for the spin-spin-energy density correlation function in the Ising model is used. The result is not a simple extension of the Fredholm structure in the Ising model.     

Efficient Hopfield pattern recognition on a scale-free neural network

Neural networks are supposed to recognise blurred images (or patterns) of N pixels (bits) each. Application of the network to an initial blurred version of one of P pre-assigned patterns should converge to the correct pattern. In the “standard" Hopfield model, the N “neurons” are connected to each other via N² bonds which contain the information on the stored patterns. Thus computer time and memory in general grow with N². The Hebb rule assigns synaptic coupling strengths proportional to the overlap of the stored patterns at the two coupled neurons. Here we simulate the Hopfield model on the Barabási-Albert scale-free network, in which each newly added neuron is connected to only m other neurons, and at the end the number of neurons with q neighbours decays as 1/q ³. Although the quality of retrieval decreases for small m, we find good associative memory for 1 ≪ m ≪ N. Hence, these networks gain a factor N/m ≫ 1 in the computer memory and time. Received 12 January 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: stauffer@thp.uni-koeln.de     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Magneto-elastic properties of Tb<Subscript>3</Subscript>Ga<Subscript>5</Subscript>O<Subscript>12</Subscript> (TGG)

The temperature dependence of the elastic constants in Tb₃Ga₅O₁₂ was measured and analysed with a simple crystal field model. The magneto-elastic coupling constants have been deduced from this experiment. The coupling constant g_Γ5, related to the c₄₄ mode, is anomalously large. These coupling constants are important for the interpretation of the phonon Hall effect.     

Synchronization,stickiness effects and intermittent oscillations in coupled nonlinear stochastic networks

Long distance reactive and diffusive coupling is introduced in a spatially extended nonlinear stochastic network of interacting particles. The network serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. If the network includes only local nearest neighbour interactions, the system organizes into a number of local asynchronous oscillators. It is shown that (a) Introduction of all-to-all coupling in the network leads the system into global, center-type, conservative oscillations as dictated by the mean-field dynamics. (b) Introduction of reactive coupling to the network leads the system to intermittent oscillations where the trajectories stick for short times in bounded regions of space, with subsequent jumps between different bounded regions. (c) Introduction of diffusive coupling to the system does not alter the dynamics for small values of the diffusive coupling p_diff, while after a critical value p_diff ^c the system synchronizes into a limit cycle with specific frequency, deviating non-trivially from the mean-field center-type behaviour. The frequency of the limit cycle oscillations depends on the reaction rates and on the diffusion coupling. The amplitude σ of the limit cycle depends on the control parameter p_diff.     

Exact solution for a degenerate Anderson impurity in the limit embedded into a correlated host

We consider the one-dimensional t - J model, which consists of electrons with spin S on a lattice with nearest neighbor hopping t constrained by the excluded multiple occupancy of the lattice sites and spin-exchange J between neighboring sites. The model is integrable at the supersymmetric point, J = t. Without spoiling the integrability we introduce an Anderson-like impurity of spin S (degenerate Anderson model in the limit), which interacts with the correlated conduction states of the host. The lattice model is defined by the scattering matrices via the Quantum Inverse Scattering Method. We discuss the general form of the interaction Hamiltonian between the impurity and the itinerant electrons on the lattice and explicitly construct it in the continuum limit. The discrete Bethe ansatz equations diagonalizing the host with impurity are derived, and the thermodynamic Bethe ansatz equations are obtained using the string hypothesis for arbitrary band filling as a function of temperature and external magnetic field. The properties of the impurity depend on one coupling parameter related to the Kondo exchange coupling. The impurity can localize up to one itinerant electron and has in general mixed valent properties. Groundstate properties of the impurity, such as the energy, valence, magnetic susceptibility and the specific heat coefficient, are discussed. In the integer valent limit the model reduces to a Coqblin-Schrieffer impurity. Received: 31 December 1997 / Accepted: 17 March 1998     

Temperature dependence of the cyclotron mass in ZnCdSe/ZnSe multi-QWs

The temperature dependence of the cyclotron resonance mass (CRM) of the magnetopolaron in ZnCdSe/ZnSe multi-quantum wells with strong magnetic field is investigated theoretically using the Lee-Low-Pines variational method. The contributions to the CRM due to the nonparabolicity of the conduction band and the coupling of electron with both confined longitudinal optical and interface optical phonons are considered. Results of our calculations are compared with the experimental data, and a qualitative agreement is found over a large temperature range. We show that these three contributions complement each other to determine the cyclotron mass as a function of the temperature.     

Buckling in a solid Langmuir monolayer: light scattering measurements and elastic model

Above a surface pressure threshold , we detect a buckled state in the low temperature solid phase of a phospholipid monolayer spread at the air-formamide interface. Stable ripples are observed with a Brewster angle microscope, and light scattering provides measurements mNm^-1, wavelength m and amplitude of a few nm for the deformation. A model, coupling the monolayer thickness and elongation, and consistent with the monolayer texture, is also presented. Received: 18 August 1997 / Revised: 9 December 1997 / Accepted: 29 January 1998     

Inclusions induced phase separation in mixed lipid film

The effect of rigid inclusions on the phase behavior of a film containing a mixture of lipid molecules is investigated. In the proposed model, the inclusion-induced deformation of the film, and the resulting energy cost are strongly dependent upon the spontaneous curvature of the mixed film. The spontaneous curvature is in turn strongly influenced by the composition of film. This coupling between the film composition and the energy per inclusion leads to a lateral modulation of the composition, which follows the local curvature of the membrane. In particular, it is shown that inclusions may induce a global phase separation in a film which would otherwise be homogeneously mixed. The mixed film is then composed of patches of different average composition, separated by the inclusions. This process may be of relevance to explain some aspects of lipid-protein association in biological membranes. Received 8 April 1999 and Received in final form 4 October 1999     

Non trivial overlap distributions at zero temperature

We explore the consequences of Replica Symmetry Breaking at zero temperature. We introduce a repulsive coupling between a system and its unperturbed ground state. In the Replica Symmetry Breaking scenario a finite coupling induces a non trivial overlap probability distribution among the unperturbed ground state and the one in presence of the coupling. We find a closed formula for this probability for arbitrary ultrametric trees, in terms of the parameters defining the tree. The same probability is computed in numerical simulations of a simple model with many ground states, but no ultrametricity: polymers in random media in 1+1 dimension. This gives us an idea of what violation of our formula can be expected in cases when ultrametricity does not hold. Received 16 June 2000