Alba Theumann

Theory of the Kondo lattice : competition between Kondo effect and magnetic order

We present here a review of some theoretical features of the Kondo lattice problem, which can describe anomalous experimental properties of strongly correlated electron systems with mainly cerium, ytterbium or uranium. In such Kondo systems, there exist both a Kondo effect on each site and strong intersite magnetic interactions. We present firstly the general case of the Kondo lattice and the mean-field approximation. We then discuss the case of the “underscreened” Kondo lattice with a strong coexistence between the Kondo effect and a ferromagnetic order, as for example observed in uranium compounds such as UTe. We also discuss the Kondo–spin glass competition with eventually an additional magnetically ordered phase (ferromagnetic or antiferromagnetic one) and we can account for phase diagrams of some cerium and uranium disordered alloys, such as CeNi1 − x Cu x . Finally, the introduction of a transverse magnetic field in the Kondo–spin glass problem yields a quantum critical point and allows a better description of the phase diagrams of disordered alloys.

The Ising spin glass in a transverse field revisited. Results of two fermionic models

We analyze the infinite 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 Siz 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 qualitatively similar results for both models. They both exhibit a critical temperature Tc(Γ) that decreases when Γ increases, until it reaches a quantum critical point at the same value of Γc and they are both unstable under replica symmetry breaking in the whole spin glass phase. Our results are in agreement with recent renormalization group calculations in three-dimensional systems.

Quantum Ising spin-glass

Abstract A random, quantum model of interacting spins, where the spin operators are represented by bilinear combinations of fermions, is studied in the Ising limit and in the static approximation. Assuming replica symmetry we recover basically the results of Sherrington and Kirkpatrick. Effects of quantum fluctuations remain in the determination of the static susceptibility χ as an independent order parameter and the breakdown of the Fischer relation.

Quantum critical point in the spin glass–Kondo transition in heavy-fermion systems

The Kondo--spin glass competition is studied in a theoretical model of a Kondo lattice with an intrasite Kondo-type exchange interaction treated within the mean-field approximation, an intersite quantum Ising exchange interaction with random couplings among localized spins, and an additional transverse field

Spin glass and ferromagnetism in Kondo lattice compounds

\ensuremath{\Gamma}

Spin glass and antiferromagnetism in Kondo-lattice disordered system

in the

Replica symmetry breaking in the transverse-field Ising spin-glass model : two fermionic representations

x

Categorization in a Hopfield network trained with weighted examples. (I). Finite number of concepts

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

Spin glass phase in Kondo lattice systems

\ensuremath{\Gamma}=\ensuremath{\alpha}{J}_{K}^{2}

Conductivity of a random electron chain renormalization group approach

(where