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

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.

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

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

Period-two cycles in a feed-forward layered neural network model with symmetric sequence processing

The effects of dominant sequential interactions are investigated in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation in which the interaction consists of a Hebbian part and a symmetric sequential term. Phase diagrams of stationary states are obtained and a new phase of cyclic correlated states of period two is found for a weak Hebbian term, independently of the number of condensed patterns $c$.Comment: 8 pages and 5 figure