= Uniform response of a two-sublattice Ising antiferromagnet
{title2=$\chi_+=\frac{\beta(1-M^2)}{1+\beta qJ(1-M^2)}$}
On the stable zero-field branch $M_B=-M_W=M$, put $a=\beta(1-M^2)$. Differentiating the <two-sublattice Ising mean-field approximation> with respect to the uniform field gives $\chi_B=a(1-qJ\chi_W)$ and $\chi_W=a(1-qJ\chi_B)$. Thus $\chi_+=a/(1+qJa)$ and $\partial M_-/\partial h=0$. The true staggered <magnetic susceptibility>, $\partial M_-/\partial g=a/(1-qJa)$, is a different response and diverges at the continuous transition. The factor $1-M^2$ is essential: the uniform response vanishes when the spins saturate at zero temperature.
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