High-temperature expansions of the staggered susceptibility for the Heisenberg antiferromagnet are analyzed for two-dimensional lattices. The evidence favoring a divergent staggered susceptibility χ̃ is found to be essentially as strong as that presented earlier in support of a divergent susceptibility χ for the two-dimensional Heisenberg ferromagnet. Thus the very recent experimental and theoretical findings which favor a phase transition in various ``planar antiferromagnets'' (or materials with the K2NiF4 structure in which the intraplanar interactions may be as much as 105 times stronger than any interplanar interactions) would appear to be supported by the series expansions. We also consider the question of the dependence of the susceptibility exponent γ[χ∼(T-Tc)−γ] upon spin quantum number S for three-dimensional lattices. The previously proposed behavior must definitely be revised in the light of additional terms in the expansions and the availability of more refined extrapolation procedures. Here we argue (a) that γ(∞)=1.38±0.01 and (b) that γ(S) does not appear to jump, for S finite, to 1.43 (its presumed value for S=½).

Stanley, H. E. (1969). Some Critical Properties of Quantum-Mechanical Heisenberg Ferro-and Antiferromagnets. Journal of Applied Physics, 40(3), 1546–1548.