= Solution
In the <Weiss molecular field> approximation, the local response obeys
$$
M=n\mu_B\tanh\!\left[\frac{\mu_B(B+\lambda\mu_0M)}{k_BT}\right].
$$
Linearize around $M=B=0$ in the stable phase of <paramagnetism>. Substitution of <3/a> gives
$$
M=\frac{C}{\mu_0T}(B+\lambda\mu_0M),\qquad
(T-\lambda C)M=\frac C{\mu_0}B.
$$
Hence the <Curie–Weiss law> and <Weiss temperature> are
$$
\boxed{\chi=\frac{C}{T-\theta},\qquad
\theta=\lambda C=\frac{\lambda n\mu_0\mu_B^2}{k_B}.}
$$
For positive $\lambda$, $\theta$ is the <mean-field theory> <Curie temperature>: the zero-magnetization solution becomes unstable there, and below it a spontaneous solution appears. For negative coupling, a negative fitted <Weiss temperature> indicates predominantly opposing interactions, but this one-uniform-magnetization treatment does not determine an antiferromagnetic ordering pattern or its transition temperature. More generally the fitted <Weiss temperature> need not equal the observed ordering temperature.
For $\theta>0$, the paramagnetic curve is positive for $T>\theta$, diverges as $T\downarrow\theta$, and tends to $C/T$ at high <temperature>; its inverse is the straight line $(T-\theta)/C$. The expression is not the stable susceptibility below $\theta$. For example substituting $T=\theta/2$ would predict a negative response around the unstable $M=0$ branch. The nonlinear self-consistency equation must instead be expanded about the appropriate spontaneous <magnetization>.
\Image[/past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2017-curie-weiss-susceptibility.png]
{title=Paramagnetic Curie-Weiss susceptibility and its inverse}
{description=The positive-Weiss-temperature mean-field law is shown only in its stable paramagnetic range $T>\theta$. Its inverse extrapolates to zero at $T=\theta$. The curve below the transition is not obtained by continuing the displayed rational expression.}
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