Theory of magnetic order in the three-dimensional spatially anisotropic Heisenberg model

A spin-rotation-invariant Green’s-function theory of long-range and short-range order (SRO) in the $S=1\mathrm{/}2$ antiferromagnetic Heisenberg model with spatially anisotropic couplings on a simple cubic lattice is presented. The staggered magnetization, the two-spin correlation functions, the correlation leng spin-rotation-invariant Green’s-function theory of long-range and short-range order (SRO) in the $S=1\mathrm{/}2$ antiferromagnetic Heisenberg model with spatially anisotropic couplings on a simple cubic lattice is presented. The staggered magnetization, the two-spin correlation functions, the correlation lengths, and the static spin susceptibility are calculated self-consistently over the whole temperature region, where the effects of spatial anisotropy are explored. As compared with previous spin-wave approaches, the N'{e}el temperature is reduced by the improved description of SRO. The maximum in the temperature dependence of the uniform static susceptibility is shifted with anisotropy and is ascribed to the decrease of SRO with increasing temperature. Comparing the theory with experimental data for the magnetization and correlation length of La${}_2$CuO${}_4$, a good agreement in the temperature dependences is obtained.