= Solution
Take the symmetric scalar <Landau free energy> with $u>0$, $r=at$ for a positive constant $a$, and leading <equation of state>
$$
H=rM+uM^3.
$$
At zero conjugate field, minimization gives $M=0$ for $t>0$ and $M=\pm\sqrt{-r/u}$ for $t<0$. Selecting the positive <pure thermodynamic phase>,
$$
M=\sqrt{\frac au}\,(-t)^{1/2}.
$$
Consequently the <order-parameter critical exponent> is $\boxed{\beta=1/2}$.
Differentiate the <equation of state> at fixed temperature, within the selected phase:
$$
\chi=\left.\frac{\partial M}{\partial H}\right|_t
=\frac1{r+3uM^2}
=\begin{cases}
(at)^{-1},&t>0,\\
(2a|t|)^{-1},&t<0.
\end{cases}
$$
Both sides diverge as $|t|^{-1}$, so the <magnetic-susceptibility critical exponent> is $\boxed{\gamma=1}$. The leading above-to-below <magnetic susceptibility> amplitude ratio is two. These are the ordinary <mean-field critical exponents>, valid under the fluctuation qualification explained above.
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