= Bounded quartic nematic coexistence
{title2=$f=6aQ^2+6bQ^3+18cQ^4$}
For $a,c>0$, $b\leq0$ and the molecular bound $Q\in[-1/2,1]$, coexistence with $Q=0$ occurs at $b_t=-\min_{0<Q\leq1}(a/Q+3cQ)$. Negative $Q$ has positive <free energy> and cannot be the stable phase in this coefficient range. Thus $a\leq3c$ gives $b_t=-\sqrt{12ac}$ and jump $0\to\sqrt{a/(3c)}$, whereas $a>3c$ gives $b_t=-(a+3c)$ and jump $0\to1$. The interior case is the usual small-order-parameter <Landau theory> result. A formal unconstrained quartic minimization can violate the molecular bounds when extrapolated too far.
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