The RKKY perturbation scheme for the spin 12 s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a...

An anisotropic generalization of the reduced s–d model with antiferromagnetically coupled impurities is proposed. This extension consists in introducing different coupling constants of s–d interaction and interimpurity coupling for spin components along the c-axis and perpendicular to the...

The Hamiltonian HK(B) of the spin 12 s-d exchange model in a uniform magnetic field B is reduced by a method previously applied to HK(0). The reduced s-d Hamiltonian Hr(B) is asymptotically equivalent in the thermodynamic limit to a mean-field hr(B), which exhibits a 2nd order phase transition...

The first- and second-order terms of a perturbation expansion of free-energy density of the s-d exchange Hamiltonian with random impurity positions, in the presence and absence of an external magnetic field B, are evaluated. The reduced s-d Hamiltonian Hr(B) is chosen for the Hamiltonian of the...

The reduced s–d model with antiferromagnetically coupled impurity spins is tested on specific heat measurements of (La1−xCex)Al2 for varying Ce concentration c and magnetic field B. The s–d exchange coupling constant J, conduction bandwidth D and coupling between impurities γ2 are...

The reduced s-d model with antiferromagnetically coupled impurity spins, previously tested on susceptibility measurements of (La1−xCex)Al2, is applied to CePd2Ga3. The s-d exchange coupling constant J, and conduction bandwidth D are adjusted to obtain the best fit of theoretical specific heat...

The thermodynamic limit of free energy density of continuous quantum systems with bounded separable 2-body interactions, confined to a compact Riemann space, is investigated. It is shown that such systems, similarly as n-particle quantum systems in a bounded region in Rv, which were discussed in...

The free energy of a classical system of interacting point particles confined to a hypersurface Σv-1r in Rv is minimized over the set of all product states corresponding to systems of noninteracting particles in equilibrium. Using techniques previously employed by Tindemans and Capel, it is...

The Feynman–Kac theorem and Bogolyubov inequality are applied to obtain a lower bound and an upper bound to the free energy of the s–d Hamiltonian with locally smeared interactions between electrons and impurities. The two bounds, which express in terms of the free energy of impurities in a...

The mean-field description previously developed for n-fermion systems in the canonical ensemble with 2-body interactions defined in the continuous configuration space of particle positions is adapted to fermion systems with bounded momentum and spin-dependent interactions. The method is applied...