Comparison of the self-consistent mean-random-field approximation with then→0expansion of Sherrington and Kirkpatrick for spin glasses and with experiment

The magnetic properties of a spin-glass system interacting with a set of Gaussian-distributed exchange potentials are obtained using the self-consistent mean-random-field (MRF) approximation. It is shown that for this distribution the magnetic properties obtained from the MRF approximation are identical with that obtained from the $n\to 0$ expansion of the free energy of Edwards and Anderson and of Sherrington and Kirkpatrick. The specific heat from the MRF approximation is also linear in temperature $T$ for low $T$. For the Ruderman-Kittel-Kasuya-Yosida interaction the $n$ expansion is difficult, however, the therymodynamic properties of the spin glasses are easily obtained in the MRF approximation. Furthermore, the latter gives some of the known properties of the system in excellent agreement with experiment. The MRF approximation predicts the following experimentally measured quantities: the low-temperature specific heat, the low-temperature low-field and high-field magnetization, the cusp in the magnetic susceptibility, the spin dependence of the susceptibility near $T\to 0$, and the low-temperature resistivity near $T\to 0$. It is furthermore argued that the scaling of the thermodynamic properties with impurity concentration will have a different concentration dependence at high and low temperatures. A possible reason for the agreement of the Ising-like model and the disagreement of the Heisenberg-like model prediction with experiment is given.