Ferromagnetic Curie Temperatures of the Heisenberg Model with Next-Nearest-Neighbor Interactions

The Curie temperatures of the Heisenberg ferromagnet with nearest-neighbor interactions -2J₁Sᵢ·Sⱼ and next-nearest-neighbor interactions -2J₂Sₖ·Sₗ are calculated for the bcc, sc, and fcc lattices on the basis of exact high-temperatures series expansions of the zero-field susceptibility χ₀. The dependence of Tc(α,S) (α=J₂J₁) on α is examined, and it is found that Tc(α)Tc(0) is well represented by Tc(α)Tc(0)=1+m₁(S)α for values of α between 0 and 1. The Curie points are also examined for α<0, where J₂ is antiferromagnetic in sign.