The spin glass-antiferromagnetism competition in Kondo-lattice systems in the presence of a transverse applied magnetic field

A theory is proposed to describe the competition among antiferromagnetism (AF), spin glass (SG) and Kondo effect. The model describes two Kondo sublattices with an intrasite Kondo interaction strength $J_{K}$ and a random Gaussian interlattice interaction in the presence of a transverse field $\Gamma$. The $\Gamma$ field is introduced as a quantum mechanism to produce spin flipping and the random coupling has average $-2J_0/N$ and variance $32 J^{2}/N$. The path integral formalism with Grassmann fields is used to study this fermionic problem, in which the disorder is treated within the framework of the replica trick. The free energy and the order parameters are obtained using the static ansatz. In this many parameters problem, we choose $J_0/J \approx (J_{K}/J)^{2}$ and $\Gamma/J \approx (J_{K}/J)^{2}$ to allow a better comparison with the experimental findings. The obtained phase diagram has not only the same sequence as the experimental one for $Ce_{2}Au_{1-x}Co_{x}Si_{3}$, but mainly, it also shows a qualitative agreement concerning the behavior of the freezing temperature and the Neel temperature which decreases until a Quantum Critical Point (QCP).Comment: 4 pages, 1 figure, accepted for publication in Physica

Fermionic Ising Glasses with BCS Pairing Interaction. Tricritical Behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric Ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J^2/N of the random couplings J_{ij}, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g_{c}(T) that ends at a tricritical point T_{3}=0.9807J, g_{3}=5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T_{c}=0.9570J that separates the NP and the SG phases. For T<T_{c} the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in Gd_{x}Th_{1-x}RU_{2}.Comment: 26 pages, 5 figures, to appear in The European Physical Journal

Feed-forward chains of recurrent attractor neural networks with finite dilution near saturation

A stationary state replica analysis for a dual neural network model that interpolates between a fully recurrent symmetric attractor network and a strictly feed-forward layered network, studied by Coolen and Viana, is extended in this work to account for finite dilution of the recurrent Hebbian interactions between binary Ising units within each layer. Gradual dilution is found to suppress part of the phase transitions that arise from the competition between recurrent and feed-forward operation modes of the network. Despite that, a long chain of layers still exhibits a relatively good performance under finite dilution for a balanced ratio between inter-layer and intra-layer interactions.Comment: To appear in Physica

Quantum critical point in the spin glass-antiferromagnetism competition for fermionic Ising Models

The competition between spin glass ($SG$) and antiferromagnetic order ($AF$) is analyzed in two sublattice fermionic Ising models in the presence of a transverse $\Gamma$ and a parallel $H$ magnetic fields. The exchange interaction follows a Gaussian probability distribution with mean $-4J_0/N$ and standard deviation $J\sqrt{32/N}$, but only spins in different sublattices can interact. The problem is formulated in a path integral formalism, where the spin operators have been expressed as bilinear combinations of Grassmann fields. The results of two fermionic models are compared. In the first one, the diagonal $S^z$ operator has four states, where two eigenvalues vanish (4S model), which are suppressed by a restriction in the two states 2S model. The replica symmetry ansatz and the static approximation have been used to obtain the free energy. The results are showing in phase diagrams $T/J$ ($T$ is the temperature) {\it versus} $J_{0}/J$, $\Gamma/J$, and $H/J$. When $\Gamma$ is increased, $T_{f}$ (transition temperature to a nonergodic phase) reduces and the Neel temperature decreases towards a quantum critical point. The field $H$ always destroys $AF$; however, within a certain range, it favors the frustration. Therefore, the presence of both fields, $\Gamma$ and $H$, produces effects that are in competition. The critical temperatures are lower for the 4S model and it is less sensitive to the magnetic couplings than the 2S model.Comment: 15 pages, 6 figures, accepted in Physica

Quantum Spherical Spin Glass.Supersymmetry and Annealing

We show that the effective action of the quantum spherical spin glass is invariant under a generalized form of the Becchi-Rouet-Stora-Tyutin(BRST) supersymmetry. The Ward identities associated to this invariance indicate that the spin glass order parameter must vanish, and as a result the annealed average is exact in this model. We present new results for for the free energy, entropy and specific heat. Due to quantum effects the entropy remains finite and the specific het vanishes at zero temperature. results for the phase diagram coincide with those obtained by different formalisms. At zero temperature we derive the scaling behaviour with frequency of the dynamical susceptibility.Comment: 17 pages, 6 figures, to be published in Phys.Rev.

Fermionic van Hemmen Spin Glass Model with a Transverse Field

In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $\Gamma$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analysis of the interplay between charge and spin fluctuations in the presence of a quantum spin flipping mechanism given by $\Gamma$. The problem is expressed in the fermionic path integral formalism. As results, magnetic phase diagrams of temperature versus the ferromagnetic interaction are obtained for several values of chemical potential $\mu$ and $\Gamma$. The $\Gamma$ field suppresses the magnetic orders. The increase of $\mu$ alters the average occupation per site that affects the magnetic phases. For instance, the SG and the mixed SG+ferromagnetic phases are also suppressed by $\mu$. In addition, $\mu$ can change the nature of the phase boundaries introducing a first order transition.Comment: 9 pages, 4 figures, accepted for publication in Phys. Lett.

Pattern reconstruction and sequence processing in feed-forward layered neural networks near saturation

The dynamics and the stationary states for the competition between pattern reconstruction and asymmetric sequence processing are studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. Earlier work by Coolen and Sherrington on a parallel dynamics far from saturation is extended here to account for finite stochastic noise due to a Hebbian and a sequential learning rule. Phase diagrams are obtained with stationary states and quasi-periodic non-stationary solutions. The relevant dependence of these diagrams and of the quasi-periodic solutions on the stochastic noise and on initial inputs for the overlaps is explicitly discussed.Comment: 9 pages, 7 figure

Fermionic Ising glasses with BCS pairing interaction in the presence of a transverse field

In the present work we have analyzed a fermionic infinite-ranged Ising spin glass with a local BCS coupling in the presence of transverse field. This model has been obtained by tracing out the conduction electrons degrees of freedom in a superconducting alloy. The transverse field \Gamma is applied in the resulting effective model. The problem is formulated in the path integral formalism where the spins operators are represented by bilinear combination of Grassmann fields. The problem can be solved by combining previous approaches used to study a fermionic Heisenberg spin glass and a Ising spin glass in a transverse field. The results are show in a phase diagram T/J {\it versus} \Gamma/J (J is the standard deviation of the random coupling J_{ij}) for several values of g (the strength of the pairing interaction). For small g, the line transition T_c(\Gamma) between the normal paramagnetic phase and the spin glass phase decreases when increases \Gamma, until it reaches a quantum critical point. For increasing g, a PAIR phase (where there is formation of local pairs) has been found which disappears when is close to \Gamma_c showing that the transverse field tends to inhibited the PAIR phase.Comment: 2 pages, 2 figures, accepted in Physica C Proceedings M2SRI