= Solution
For the requested ordinary critical point take $u>0$, $r=r_0t$, and the quartic <Landau free energy> $U(M)=rM^2/2+uM^4/4-hM$. At $h=0,t<0$, minimization gives $M^2=-r/u$. Choosing the positive <pure thermodynamic phase>,
$$
M=\sqrt{\frac{r_0}{u}}(-t)^{1/2},\qquad \boxed{\beta=\frac12.}
$$
For the <magnetic susceptibility>, differentiate the equation of state at fixed temperature:
$$
1=(r+3uM^2)\frac{\partial M}{\partial h},\qquad
\chi=\begin{cases}(r_0t)^{-1},&t>0,\\ (2r_0|t|)^{-1},&t<0\text{ on a selected phase}.\end{cases}
$$
Both sides diverge as $|t|^{-1}$, with different amplitudes, so
$$
\boxed{\gamma=1.}
$$
The one-sided field limit below the transition selects a pure phase; differentiating the symmetric finite-volume mixture would instead include its macroscopic switching response.
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