PAIR APPROXIMATION TO THE RUDERMAN-KITTEL-KASUYA-YOSHIDA FREE-ENERGY

The free energy of the Ruderman-Kittel-Kasuya-Yoshida (RKKY) model of spin glasses is calculated in the pair approximation. Correlations between nearest neighbor spins are evaluated exactly. After factorization of the total partition function into pair states, the free energy is obtained as an analytical function of the external variables (T, H, C). Particular care is taken in the evaluation of (i) the ensemble average over a quenched random RKKY system and (ii) the quantum mechanical effects depending on the spin value S. The free energy obeys the well-known scaling laws in the dilute limit C ≲ 1000 ppm. An approach to the problem of deviations from scaling is also indicated. The relation of the pair approximation to the first terms in the virial expansion is discussed. The theory has a broad field of application to all thermodynamic (time-independent) measurements, with semiquantitative results in the paramagnetic domain. Time-dependent blocking phenomena are not obtained within this approximation, but it is argued that the contribution of local correlations (freezing) to the total free energy is also important below the blocking temperature. © 1979 Plenum Publishing Corporation.