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 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=αJ²K (where JK 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 QCPs. The existence of a QCP in the spin glass–Kondo competition allows one to give a better description of the phase diagrams of some cerium and uranium disordered alloys