= Solution
In the usual three-dimensional isotropic setting, the transition is expected to be \b[discontinuous], by the <Brazovskii fluctuation-induced first-order transition> mechanism.
If $\bar\kappa<0$, write $q_*^2=-\bar\kappa/(2\gamma)$ and $r=\bar a-\bar\kappa^2/(4\gamma)$. Then $J(q)=r+\gamma(q^2-q_*^2)^2$. A continuous finite-wavevector transition would require $r\to0$ with $q_*>0$. But the <soft-mode shell integral> behaves as
$$
\int\frac{d^3q}{(2\pi)^3J(q)}\sim\frac{q_*}{4\pi\sqrt{\gamma r}},
\qquad
\int\frac{q^2\,d^3q}{(2\pi)^3J(q)}\sim\frac{q_*^3}{4\pi\sqrt{\gamma r}}.
$$
The positive fluctuation corrections in the <self-consistency equations> diverge in that limit. In particular $\bar\kappa=\kappa+2BI_0$ cannot stay at a finite negative value while $I_0$ diverges. Thus the isotropic disordered state cannot lose stability through a zero-mass mode on a fixed nonzero shell in this approximation.
Ordering is instead expected through a free-energy crossing with a finite-amplitude <smectic phase>, giving a <first-order phase transition>. This is a reasoned fluctuation prediction for the finite-wavevector transition; the disordered <Gaussian variational approximation> alone does not locate the coexistence point or calculate the amplitude jump. A zero-wavevector instability or a lower-dimensional setting would require a separate analysis.
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