Perturbation Treatment of the Antiferromagnetic Ground State

Ground-state parameter series expansions are generated for the Heisenberg model of antiferromagnetism. These expansions are taken about the Ising model, and the terms are expressed as analytic functions of the spin for the linear chain, plane quadratic, simple cubic, body-centered cubic, and hypercubic lattices. Energy, short-range order, and sublattice magnetization series are given through fourth order in the transverse spin operators, and numerical values are calculated for these terms in the cases of the linear chain, plane quadratic, simple cubic, and body-centered cubic lattices with $2S=1, 2, 3, 4, 5$. Comparison is made with the ground-state parameter series developed for a spin-wave theory with Ising anisotropy, and an "overlap" contribution common to both treatments is defined. It is found that the disagreement between the spin-wave theory of the ground-state sublattice magnetization and the experimental results for KMn${\mathrm{F}}_3$ and Mn${\mathrm{F}}_2$ is not contradicted by our perturbation treatment.