The Néel temperature of a D-dimensional bcc Heisenberg antiferromagnet

The double-time temperature-dependent Green’s function method is used to determine the Néel temperature of a Heisenberg antiferromagnet with easy axis XXZ anisotropy on a D-dimensional bcc lattice. Exact equations within the random phase approximation (RPA) and Callen approximation (CA) in terms of generalized hypergeometric functions valid for arbitrary D, S, and η≥1 are given. Analytical and numerical results presented here strongly suggest that, for D≥2, the CA gives a higher critical temperature. It is also shown that the RPA set of self-consistent equations yields a Néel temperature closer to the experimental value for compound (CH3NH3)2MnCl4.