= Solution
At a <tricritical point>, both $r$ and $u$ vanish, while $v>0$ stabilizes the <Landau free energy>. It separates ordinary continuous transitions for $u>0$ from first-order coexistence for $u<0$. The zero-field order-parameter jump shrinks to zero as $u\uparrow0$, and the <tricritical wings> terminate there in the full $(r,u,h)$ diagram. For $r<0$, $u=0$, minimizing gives $M^4=-r/v$ and
$$
V(M_0)=-\frac{|r|^{3/2}}{3\sqrt v}.
$$
Two thermal derivatives give the <heat-capacity critical exponent> $\alpha=1/2$, compared with the finite mean-field heat-capacity jump, $\alpha=0$, at an ordinary quartic transition. The remaining tricritical <mean-field critical exponents> are $(\beta,\gamma,\delta)=(1/4,1,5)$, and the mean-field <correlation-length critical exponent> is $\nu=1/2$. To observe tricritical scaling one must tune the quartic scaling field as well as the thermal field: a generic path with fixed $u>0$ instead has ordinary critical behavior. Its <upper critical dimension> is three, as the <multicritical Ginzburg ratio> shows.
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