= Solution
For $u>0$, the quartic <Landau free energy> at $h=0$ minimizes at $m=0$ for $r>0$ and at $m=\pm\sqrt{-r/u}$ for $r<0$. The <order parameter> changes continuously at $r=0$, giving a <continuous phase transition> and a divergent response. The minimized potential is $0$ above the transition and $-r^2/(4u)$ below it, so its first temperature derivative is continuous while its second derivative jumps.
For $u<0$, retain $v>0$. A <first-order phase transition> occurs when the $m=0$ minimum and a nonzero minimum have equal free energy. Combining stationarity $r+um^2+vm^4=0$ with equality of potential values gives
$$
\boxed{m^2=-\frac{3u}{4v},\qquad r=\frac{3u^2}{16v}.}
$$
The order parameter jumps at a positive $r$ before the disordered minimum loses local stability. Generic temperature dependence then also produces a jump in entropy and a <latent heat>. Equality of global minima locates coexistence; the disappearance of a metastable minimum instead defines a <spinodal point>.
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