A theory is presented that describes a spin-glass phase at finite temperatures in Kondo-lattice systems with an additional Ruderman-Kittel-Kasuya-Yosida interaction represented by long range, random couplings among localized spins as in the Sherrington-Kirkpatrick ͑SK͒ spin-glass model. The problem is studied within the functional integral formalism where the spin operators are represented by bilinear combinations of fermionic ͑anticommuting͒ Grassmann variables. The Kondo and spin-glass transitions are both described with the mean-field-like static ansatz that reproduces good results in the two well-known limits. At high temperatures and low values of the Kondo coupling there is a paramagnetic ͑disordered͒ phase with vanishing Kondo and spin-glass order parameters. By lowering the temperature, a second order transition line is found at T SG to a spin-glass phase. For larger values of the Kondo coupling there is a second order transition line at roughly T k to a Kondo ordered state. For TϽT SG the transition between the Kondo and spin-glass phases becomes first order.

We analyze the long range Ising spin glass in a transverse field Γ by using Grassmann variables in a field theory where the spin operators are represented by bilinear combinations of fermionic fields. We compare the results of two fermionic models. In the four state (4S)-model the diagonal S z i operator has two vanishing eigenvalues, that are suppressed by a restraint in the two states (2S)-model. Within a replica symmetric theory and in the static approximation we obtain similar results for both models. They both exhibit a critical temperature T c (Γ) that decreases when Γ increases, until it reaches a quantum critical point (QCP) at the same value of Γ c and they are both unstable under replica symmetry breaking in the whole spin glass phase.

The competition between spin glass (SG), antiferromagnetism (AF) and Kondo effect is studied here in a model which consists of two Kondo sublattices with a gaussian random interaction between spins in differents sublattices with an antiferromagnetic mean Jo and standard deviation J. In the present approach there is no hopping of the conduction electrons between the sublattices and only spins in different sublattices can interact. The problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields which can be solved at mean field level within the static approximation and the replica symmetry ansatz. The obtained phase diagram shows the sequence of phases SG, AF and Kondo state for increasing Kondo coupling. This sequence agrees qualitatively with experimental data of the Ce2Au1−xCoxSi3 compound.PACS. 05.50.+q Lattice theory and statistics; Ising problems -64.60.Cn Order disorder transformations; statistical mechanics of model systems

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin

The Kondo-Spin Glass competition is studied in a theoretical model of a Kondo lattice with an intra-site Kondo-type exchange interaction treated within the mean-field approximation, an inter-site quantum Ising exchange interaction with random couplings among localized spins and an additional transverse field Γ in the x-direction, which represents a simple quantum mechanism of spin flipping, in order to have a better description of the spin-glass state and in particular of the Quantum Critical Point(QCP). Taking here a parametrization Γ = αJ 2 K (where J K is the antiferromagnetic Kondo coupling), we obtain two second order transition lines from the spin-glass state to the paramagnetic one and then to the Kondo-state. For a reasonable set of the different parameters, the two second order transition lines do not intersect and end in two distinct QCP. The existence of QCP in the Spin Glass-Kondo competition allows to give a better description of the phase diagrams of some Cerium and Uranium disordered alloys.