The coherent potential approximation and the diagrammatic 1/Z expansion for an anisotropic spin-1 paramagnet

Abstract

The magnetic Green functions in the paramagnetic phase or a dilute of a binary alloy system are calculated for arbitrary concentrations of magnetic ions. The calculation employs a diagrammatic perturbation formalism based on the use of semi-invariants. Specifically, the theory is applied to S=1 systems in both the easy-axis and the easy-planar cases. The approximation made in the theory is basically to consider the ions as separate entities embedded in an effective medium, which is established in a self-consistent fashion. The calculated self-energy of the Green functions contains both the CPA contributions, due to the inhomogeneities, and the contributions from the fourth-order semi-invariants of the single spins appearing in order 1/Z in the high-density expansion. The behaviour of the effective single-site Green function is analysed in detail. The spurious divergence of this quantity in the order (1/Z)0, which leads to unphysical results in the dilute limit, is found to be much suppressed.