The Néel temperature of a DD-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 XXZXXZ anisotropy on a DD-dimensional bcc lattice. Exact equations within the random phase approximation (RPA) and Callen approximation (CA) in terms of generalized hypergeometric functions valid for arbitrary DD, SS, and η≥1η≥1 are given. Analytical and numerical results presented here strongly suggest that, for D≥2D≥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.

► Tyablikov’s and Callen’s methods are compared.
► The Néel temperature is determined by using DD-dimensional Watson-like integrals.
► Exact solutions in terms of generalized hypergeometric function are given.
► Callen’s approach yields higher critical temperature for D≥2D≥2.
► Tyablikov’s method gives Néel temperature closer to the experimental value for compoung (CH3NH3)2MnCl4.