Magnetic phase transitions in randomly diluted fcc spin system with competing interactions: The case with ferromagnetic J1 and arbitrary J2.

The randomly diluted Heisenberg paramagnet, with nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange coupling of arbitrary sign, is analyzed using the technique of high-temperature series expansion. The paramagnetic susceptibility is evaluated to seventh order in the inverse power of the temperature. By utilizing the series, an analysis of an fcc lattice with NN ferromagnetic coupling ${\mathit{J}}_{1}$ and NNN antiferromagnetic coupling ${\mathit{J}}_{2}$ is carried out. This model corresponds to the well-known spin-glass system ${\mathrm{Eu}}_{\mathit{c}}$${\mathrm{Sr}}_{1\mathrm{\ensuremath{-}}\mathit{c}}$S, with a magnetic-constituent-atom concentration c\ensuremath{\le}1. The series is analyzed via the coherent-anomaly method and estimates for the transition temperature ${\mathit{T}}_{\mathit{c}}$ and the concentration-dependent effective exponent for the susceptibility, ${\ensuremath{\gamma}}_{\mathit{e}\mathit{f}\mathit{f}}$, are obtained for various values of the ratio \ensuremath{\alpha}=${\mathit{J}}_{2}$/${\mathit{J}}_{1}$ and the concentration c. The results are similar to those obtained by a Monte Carlo procedure as discussed by Binder, Kinzel, and Stauffer.