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

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

Spin Glass and ferromagnetism in disordered Kondo lattice

The competition among spin glass (SG), ferromagnetism and Kondo effect has been analysed in a Kondo lattice model where the inter-site coupling $J_{ij}$ between the localized magnetic moments is given by a generalized Mattis model \cite{Mattis} which represents an interpolation between ferromagnetism and a highly disordered spin glass. Functional integral techniques with of Grassmann fields has been used to obtain the partition function. The static approximation and the replica symmetric ansatz has also been used. The solution of the problem is presented as a phase diagram temperature $T$ {\it versus} $J_K$ (the strength of the intra-site interaction). If $J_K$ is small, for decreasing temperature there is a second order transition from a paramagnetic to a spin glass phase For lower temperatures, a first order transition appears where solutions for the spin glass order parameter and the local magnetizations are simultaneously non zero. For very low temperatures, the local magnetizations becomes thermodinamically stables. For high $J_K$, the Kondo state is dominating. These results could be helpful to clarify the experimental situation of $CeNi_{1-x}Cu_{x}$.Comment: 4 pages, 1 figure, accept to be published in Physica

A theoretical study of the cluster glass-Kondo-magnetic disordered alloys

The physics of disordered alloys, such as typically the well known case of CeNi1-xCux alloys, showing an interplay among the Kondo effect, the spin glass state and a magnetic order, has been studied firstly within an average description like in the Sherrington-Kirkpatrick model. Recently, a theoretical model (PRB 74, 014427 (2006)) involving a more local description of the intersite interaction has been proposed to describe the phase diagram of CeNi1-xCux. This alloy is an example of the complex interplay between Kondo effect and frustration in which there is in particular the onset of a cluster-glass state. Although the model given in Ref. PRB 74, 014427 (2006) has reproduced the different phases relatively well, it is not able to describe the cluster-glass state. We study here the competition between the Kondo effect and a cluster glass phase within a Kondo Lattice model with an inter-cluster random Gaussian interaction. The inter-cluster term is treated within the cluster mean-field theory for spin glasses, while, inside the cluster, an exact diagonalisation is performed including inter-site ferromagnetic and intra-site Kondo interactions. The cluster glass order parameters and the Kondo correlation function are obtained for different values of the cluster size, the intra-cluster ferromagnetic coupling and the Kondo intra-site coupling. We obtain, for instance, that the increase of the Kondo coupling tends to destroy the cluster glass phase.Comment: 6 pages, 2 figures, Accepted for publication in Physica

Investigation of mass and energy coupling between soot particles and gas species in modelling counterflow diffusion flames

A numerical model is developed aiming at investigating soot formation in ethylene counterflow diffusion flames at atmospheric pressure. In order to assess modeling limitations the mass and energy coupling between soot solid particles and gas-phase species are investigated in detail. A semi-empirical two equation model based on acetylene as the soot precursor is chosen for predicting soot mass fraction and number density. For the solid-phase the model describes particle nucleation, surface growth and oxidation. For the gas-phase a detailed kinetic mechanism is considered. Additionally, the effect of considering gas and soot radiation heat losses is evaluated in the optically thin limit approximation. The results show that for soot volume fractions higher than a certain threshold value the formation of the solid particles begins to significantly influence the gas-phase composition and temperature. The results also show that the inclusion of radiant heat losses decreases this influence. Keywords: Combustion, Soot model, Coupling effect, Counterflow flame

Stability conditions for fermionic Ising spin-glass models in the presence of a transverse field

The stability of spin-glass (SG) phase is analyzed in detail for a fermionic Ising SG (FISG) model in the presence of a magnetic transverse field $\Gamma$. The fermionic path integral formalism, replica method and static approach have been used to obtain the thermodynamic potential within one step replica symmetry breaking ansatz. The replica symmetry (RS) results show that the SG phase is always unstable against the replicon. Moreover, the two other eigenvalues $\lambda_{\pm}$ of the Hessian matrix (related to the diagonal elements of the replica matrix) can indicate an additional instability to the SG phase, which enhances when $\Gamma$ is increased. Therefore, this result suggests that the study of the replicon can not be enough to guarantee the RS stability in the present quantum FISG model, especially near the quantum critical point. In particular, the FISG model allows changing the occupation number of sites, so one can get a first order transition when the chemical potential exceeds a certain value. In this region, the replicon and the $\lambda_{\pm}$ indicate instability problems for the SG solution close to all range of first order boundary.Comment: 15 pages, 4 figures, accepted 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

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.

Doniach diagram for ordered, disordered and underscreened Kondo lattices

The Doniach's diagram has been originally proposed to describe the competition between the local Kondo effect and the intersite RKKY interactions in cerium compounds. Here we discuss the extension of this diagram to different variations of Kondo lattice model. We consider a) ordered cerium compounds where the competition between magnetic order and Kondo effect plays an important role, as $CeRh_2Si_2$, b) disordered cerium systems with competing spin glass phase, magnetic ordered phases and a Kondo phase, as the heavy fermion cerium alloy $CeCu_xNi_{1-x}$ and, c) uranium compounds where a coexistence between Kondo effect and ferromagnetic order has been observed, as UTe. We show that all these cases can be described by a generalized Doniach phase diagram.Comment: Presented in the Latin American Workshop on Magnetism and Magnetic Materials (LAW3M) Rio de Janeiro, Brazil, August 12-16, 2007. Proceedings to be published in JMM

Modeling magnetospheric fields in the Jupiter system

The various processes which generate magnetic fields within the Jupiter system are exemplary for a large class of similar processes occurring at other planets in the solar system, but also around extrasolar planets. Jupiter's large internal dynamo magnetic field generates a gigantic magnetosphere, which is strongly rotational driven and possesses large plasma sources located deeply within the magnetosphere. The combination of the latter two effects is the primary reason for Jupiter's main auroral ovals. Jupiter's moon Ganymede is the only known moon with an intrinsic dynamo magnetic field, which generates a mini-magnetosphere located within Jupiter's larger magnetosphere including two auroral ovals. Ganymede's magnetosphere is qualitatively different compared to the one from Jupiter. It possesses no bow shock but develops Alfv\'en wings similar to most of the extrasolar planets which orbit their host stars within 0.1 AU. New numerical models of Jupiter's and Ganymede's magnetospheres presented here provide quantitative insight into the processes that maintain these magnetospheres. Jupiter's magnetospheric field is approximately time-periodic at the locations of Jupiter's moons and induces secondary magnetic fields in electrically conductive layers such as subsurface oceans. In the case of Ganymede, these secondary magnetic fields influence the oscillation of the location of its auroral ovals. Based on dedicated Hubble Space Telescope observations, an analysis of the amplitudes of the auroral oscillations provides evidence that Ganymede harbors a subsurface ocean. Callisto in contrast does not possess a mini-magnetosphere, but still shows a perturbed magnetic field environment. Callisto's ionosphere and atmospheric UV emission is different compared to the other Galilean satellites as it is primarily been generated by solar photons compared to magnetospheric electrons.Comment: Chapter for Book: Planetary Magnetis